chunk_uid stringlengths 40 40 | chunk_type stringclasses 2
values | chunk_index int64 0 6.71k | total_chunks int64 1 6.71k | section_title stringlengths 1 157 | embed_text stringlengths 1 83.3k | spans dict | paper_doi stringlengths 0 63 | paper_id_arxiv stringlengths 9 16 | title stringlengths 7 245 | authors listlengths 1 768 | categories listlengths 1 7 | year int64 2k 2.02k | language stringclasses 2
values | discipline stringclasses 8
values | sparse_indices listlengths 1 1.02k | sparse_values listlengths 1 1.02k |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0c6fcbdd0cb2919788e0a62b3ba92697d7bdf9dc | subsection | 11 | 17 | Individual sources | The timescale is not
seen in DCF analysis of Paper I, probably because even though there are some
flares with 3.5 years between them, it is not a timescale clearly seen to
repeat in the flux curve.PKS 1749+096:
This BLO type object has been monitored in Metsähovi for 20 years at
22 GHz and 25 years at 37 GHz. At 90 GHz... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 430,
"openalex_id": "",
"raw": "Homan, D. C., Ojha, R., Wardle, J. F. C., et al. 2001, , 549, 840",
"source_ref_id": "82b3060b66c2734e7add271ee2d9d4d519c72420",
"start": 354
},
{
"arxiv_id": "",
"do... | 10.1051/0004-6361:200810200 | 0807.1796 | Wavelet analysis of a large sample of AGN at high radio frequencies | [
"T. Hovatta",
"H. J. Lehto",
"M. Tornikoski"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
20028,
57965,
83,
959,
51592,
31455,
919,
114137,
62323,
87,
4,
31895,
6637,
21208,
621,
3060,
12564,
68291,
678,
38704,
5369,
17721,
123019,
119140,
85679,
9709,
272,
47386,
294,
729,
12977,
138790,
11648,
3293,
335,
17014,
10644,
36746,
1... | [
0.2137451171875,
0.3037109375,
0.047210693359375,
0.1448974609375,
0.2039794921875,
0.116943359375,
0.15380859375,
0.22509765625,
0.2255859375,
0.147705078125,
0.00897216796875,
0.0645751953125,
0.002532958984375,
0.003753662109375,
0.009185791015625,
0.0244903564453125,
0.1799316406... |
8008dd67b78344150a27046cc72a31e1fbfc36cf | subsection | 12 | 17 | Discussion | Our interest in using wavelets to study the timescales arose from the
results of Paper I, which showed that many of the sources have
changed their behaviour during the monitoring time and the timescales
have changed over the years. A useful property of wavelets is that
they show also when the timescale has been present... | {
"cite_spans": []
} | 10.1051/0004-6361:200810200 | 0807.1796 | Wavelet analysis of a large sample of AGN at high radio frequencies | [
"T. Hovatta",
"H. J. Lehto",
"M. Tornikoski"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
22929,
33946,
17368,
259,
2601,
7831,
47,
35187,
70,
20028,
57965,
7,
10,
75287,
50339,
62323,
87,
4,
3129,
168360,
450,
5941,
111,
97264,
765,
98816,
2363,
224833,
20271,
97204,
1733,
645,
5369,
80234,
57266,
83,
1836,
7639,
2843,
3229,
... | [
0.0198822021484375,
0.1490478515625,
0.1114501953125,
0.2071533203125,
0.262939453125,
0.263427734375,
0.03717041015625,
0.1632080078125,
0.0372314453125,
0.1827392578125,
0.28564453125,
0.0638427734375,
0.037261962890625,
0.0255279541015625,
0.0711669921875,
0.1412353515625,
0.09503... |
eafe3d1f7c880c153875cb5f408117fb4d7d9843 | subsection | 13 | 17 | Discussion | REF ) and multiple timescales are seen.
[Figure: Upper panel: Long-term wavelet timescale against the DCF timescale from Paper I. Lower panel: The same wavelet timescale against the Lomb-Scargle periodogram timescale from Paper I.]The average timescales of wavelet and DCF analyses are also very similar
with the differe... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 799,
"openalex_id": "",
"raw": "Kelly, B. C., Hughes, P. A., Aller, H. D., & Aller, M. F. 2003, ApJ, 591, 695",
"source_ref_id": "15e6c5fc946fb1b681e6ab2d29be2bf9c6a00016",
"start": 692
},
{
"arxiv_id": "... | 10.1051/0004-6361:200810200 | 0807.1796 | Wavelet analysis of a large sample of AGN at high radio frequencies | [
"T. Hovatta",
"H. J. Lehto",
"M. Tornikoski"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
9069,
919,
136,
48716,
20028,
57965,
7,
621,
51592,
5,
6159,
6795,
13,
12,
26655,
56,
16138,
14407,
9,
32166,
259,
2601,
126,
26548,
70,
31455,
62323,
87,
61187,
581,
5701,
2091,
6492,
294,
3284,
15592,
21318,
25561,
3957,
83080,
111,
... | [
0.06536865234375,
0.1910400390625,
0.043304443359375,
0.1751708984375,
0.2010498046875,
0.2890625,
0.03204345703125,
0.032318115234375,
0.123291015625,
0.031982421875,
0.01092529296875,
0.021240234375,
0.03179931640625,
0.03131103515625,
0.034423828125,
0.032135009765625,
0.110717773... |
8b1aba017dc0751de81bd7c49193a166f69aa292 | subsection | 14 | 17 | Conclusions | We studied a sample of 80 sources with the continuous wavelet transform
using data at 22, 37 and 90 GHz. Our aim was to study the variability
behaviour of the sources and also to better
understand the method and to compare it
with Fourier-based methods. We found no clear periodicities in the
sources. Instead in most of... | {
"cite_spans": []
} | 10.1051/0004-6361:200810200 | 0807.1796 | Wavelet analysis of a large sample of AGN at high radio frequencies | [
"T. Hovatta",
"H. J. Lehto",
"M. Tornikoski"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
1401,
22282,
71,
10,
121413,
111,
2248,
97264,
62005,
223,
259,
2601,
126,
27198,
17368,
2053,
99,
24470,
4669,
136,
2510,
117690,
464,
509,
35187,
70,
141796,
2481,
224833,
47,
11522,
28219,
55300,
69101,
442,
65056,
6815,
9,
77007,
1506... | [
0.019775390625,
0.1439208984375,
0.029937744140625,
0.029815673828125,
0.2021484375,
0.0298919677734375,
0.205078125,
0.26171875,
0.1839599609375,
0.02838134765625,
0.1868896484375,
0.2203369140625,
0.20068359375,
0.2349853515625,
0.014129638671875,
0.1307373046875,
0.03887939453125,... |
4c456077e4dba1c98fbc14856bf62f837ef0a124 | subsection | 15 | 17 | Conclusions | If more than one timescale is given the most significant one is placed first.4c22 GHz 4c37 GHz 4c90 GHzB1950 Other Class monitoring time cycles flare monitoring time cycles flare monitoring time cycles flarename name time [yr] scale [yr] scale [yr] time [yr] scale [yr] scale [yr] time [yr] scale [yr] scale [yr]Continue... | {
"cite_spans": []
} | 10.1051/0004-6361:200810200 | 0807.1796 | Wavelet analysis of a large sample of AGN at high radio frequencies | [
"T. Hovatta",
"H. J. Lehto",
"M. Tornikoski"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
4263,
1286,
3501,
1632,
20028,
57965,
83,
34475,
70,
2684,
88551,
158012,
5117,
5,
617,
238,
4015,
117690,
201,
10945,
5039,
571,
113108,
64511,
35014,
97204,
1733,
105823,
7,
12564,
1046,
11627,
9351,
12271,
268,
105994,
378,
100761,
297,
... | [
0.10516357421875,
0.130126953125,
0.12890625,
0.1199951171875,
0.2401123046875,
0.34814453125,
0.0672607421875,
0.1405029296875,
0.06622314453125,
0.166259765625,
0.2705078125,
0.2130126953125,
0.2227783203125,
0.0789794921875,
0.1341552734375,
0.06658935546875,
0.1583251953125,
0.... |
de8a1b1aa76602bbb38bc707439d2044f2635fa7 | subsection | 16 | 17 | Conclusions | N = not enough data for wavelet analysis. | {
"cite_spans": []
} | 10.1051/0004-6361:200810200 | 0807.1796 | Wavelet analysis of a large sample of AGN at high radio frequencies | [
"T. Hovatta",
"H. J. Lehto",
"M. Tornikoski"
] | [
"astro-ph"
] | 2,008 | en | Physics | [
541,
2203,
959,
20174,
2053,
100,
259,
2601,
126,
114137,
5
] | [
0.1846923828125,
0.15380859375,
0.1763916015625,
0.1871337890625,
0.22265625,
0.04827880859375,
0.172607421875,
0.1380615234375,
0.2109375,
0.2279052734375,
0.0020751953125
] |
a0905a40600d30cb3e2f347de386fe0f1b4fd26f | abstract | 0 | 11 | Abstract | We consider a modified gravity fluid on a Randall-Sundrum II brane situated
at y=0, the action containing a power \alpha of the scalar curvature. As is
known from 4D spatially flat modified gravity, the presence of a bulk viscosity
may drive the cosmic fluid into the phantom region (w < -1) and thereafter
inevitably in... | {
"cite_spans": []
} | 10.1140/epjc/s10052-008-0678-3 | 0807.1797 | Viscous Modified Gravity on a RS Brane Embedded in AdS5 | [
"Iver Brevik"
] | [
"gr-qc"
] | 2,008 | en | Physics | [
16916,
73197,
297,
64002,
939,
79552,
39643,
5584,
66279,
131453,
1995,
1620,
86,
39501,
99,
113,
145407,
22631,
70541,
14537,
289,
14612,
146232,
42,
130661,
6644,
51529,
201,
397,
5623,
49878,
169424,
11876,
92,
4498,
7840,
2481,
1543,
22... | [
0.05303955078125,
0.1881103515625,
0.032257080078125,
0.2044677734375,
0.07373046875,
0.250732421875,
0.0850830078125,
0.179443359375,
0.056365966796875,
0.255859375,
0.16455078125,
0.1617431640625,
0.1680908203125,
0.08709716796875,
0.0253753662109375,
0.0482177734375,
0.17541503906... |
14a5150984ad3f1ead9b6bbbc206a0203ce11884 | subsection | 1 | 11 | Introduction | Modified gravity theories in 4D continue to attract interest; this
obviously being related to observations, for instance the measured
redshifts from type Ia supernovae
, , . The data may be reconciled
with the concept of dark energy, with a cosmic fluid with a
complicated equation of state, or with a scalar field havin... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 173,
"openalex_id": "",
"raw": "A. G. Reiss et al., Astron. J. 116, 1009 (1998).",
"source_ref_id": "37aac48d07285024197c3a11d6b3bbae240b733e",
"start": 0
},
{
"arxiv_id": "",
"doi": "",
"end"... | 10.1140/epjc/s10052-008-0678-3 | 0807.1797 | Viscous Modified Gravity on a RS Brane Embedded in AdS5 | [
"Iver Brevik"
] | [
"gr-qc"
] | 2,008 | en | Physics | [
16269,
47314,
64002,
939,
3790,
10484,
23,
201,
397,
21342,
110281,
33946,
171259,
8035,
62548,
47,
150556,
7,
4,
100,
70,
72350,
71,
4842,
3767,
2480,
10644,
12044,
1601,
10167,
6,
2053,
1543,
186,
44188,
318,
6259,
678,
23755,
111,
43... | [
0.176025390625,
0.160888671875,
0.2178955078125,
0.0994873046875,
0.2076416015625,
0.1053466796875,
0.0196380615234375,
0.1783447265625,
0.208740234375,
0.06451416015625,
0.0848388671875,
0.0775146484375,
0.029632568359375,
0.01666259765625,
0.025115966796875,
0.0195159912109375,
0.1... |
2000e994e252c427e72485384861723b32ee2a60 | subsection | 2 | 11 | Basic formalism | Assume, as mentioned, that there is a spatially flat (k=0)
brane located at the fifth dimension y=0, surrounded by an
Anti-de Sitter (AdS) space. If the five-dimensional cosmological
constant \Lambda (<0) is different from zero, this model is the
Randall-Sundrum II model (RSII) . We
shall take the metric to have the fo... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 280,
"openalex_id": "",
"raw": "L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999).",
"source_ref_id": "acfd1afd21e2dc42a16535baf7bf97120a5dd3ba",
"start": 146
},
{
"arxiv_id": "",
"doi": "... | 10.1140/epjc/s10052-008-0678-3 | 0807.1797 | Viscous Modified Gravity on a RS Brane Embedded in AdS5 | [
"Iver Brevik"
] | [
"gr-qc"
] | 2,008 | en | Physics | [
66596,
13,
237,
119056,
2685,
83,
5623,
118,
25958,
49878,
92,
145407,
1620,
86,
105866,
99,
70,
809,
2480,
127,
6,
91403,
113,
4,
613,
42,
167457,
142,
8332,
112,
602,
3055,
22409,
294,
16,
32628,
4263,
43606,
157955,
9545,
39,
10962... | [
0.11474609375,
0.03155517578125,
0.0172271728515625,
0.038726806640625,
0.030426025390625,
0.056182861328125,
0.10595703125,
0.036956787109375,
0.0911865234375,
0.2244873046875,
0.0128173828125,
0.17919921875,
0.1881103515625,
0.203369140625,
0.1348876953125,
0.0204315185546875,
0.04... |
55e2881d906706fb764bc2bcff8c9bc0e26fccc1 | subsection | 3 | 11 | Basic formalism | As the 5D space outside the brane is taken to be
empty, the components of T_{AB} are different from zero only on
the brane.Consider next the form of T_{AB}. Let U^\mu =(U^0, U^i) (Greek
indices \mu ,\nu \in [0,3]) be the fluid's four-velocity on the
brane, and let \sigma denote the brane tension, assumed
constant. More... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 752,
"openalex_id": "",
"raw": "S. Nojiri and S. D. Odintsov, Phys. Rev. D 72, 023003 (2005).",
"source_ref_id": "027341187ffa723feb1e8e671d84ee7c7ef85ea0",
"start": 601
},
{
"arxiv_id": "",
"doi": ... | 10.1140/epjc/s10052-008-0678-3 | 0807.1797 | Viscous Modified Gravity on a RS Brane Embedded in AdS5 | [
"Iver Brevik"
] | [
"gr-qc"
] | 2,008 | en | Physics | [
1301,
190,
397,
32628,
50782,
70,
1620,
86,
39958,
47,
186,
201505,
82761,
111,
384,
454,
11040,
8152,
621,
12921,
1295,
45234,
4734,
98,
30542,
11737,
3173,
10842,
345,
8353,
561,
2389,
4,
14,
91127,
136044,
539,
96386,
79552,
22759,
1... | [
0.03515625,
0.160400390625,
0.1669921875,
0.1895751953125,
0.1688232421875,
0.0408935546875,
0.1846923828125,
0.1785888671875,
0.05889892578125,
0.00494384765625,
0.022796630859375,
0.1690673828125,
0.2127685546875,
0.0309906005859375,
0.1766357421875,
0.101806640625,
0.254150390625,... |
3e013518803c54cca916c306f5cf6ead2ea59c00 | subsection | 4 | 11 | Basic formalism | It implies thatn(t,y)=\frac{\dot{a}(t,y)}{\dot{a}_0(t)}for arbitrary y. Then from Eq. (REF ) we get, upon
integration with respect to y,\left(\frac{\dot{a}}{na}\right)^2=\frac{1}{6}\Lambda +\left(\frac{a^{\prime }}{a}\right)^2+\frac{C}{a^4}.Here C=C(t) is an integration constant with respect to y. The
C term is called ... | {
"cite_spans": []
} | 10.1140/epjc/s10052-008-0678-3 | 0807.1797 | Viscous Modified Gravity on a RS Brane Embedded in AdS5 | [
"Iver Brevik"
] | [
"gr-qc"
] | 2,008 | en | Physics | [
1650,
35388,
90,
19,
18,
53,
1369,
132076,
15464,
11,
2389,
2472,
61799,
113,
864,
11766,
919,
2046,
54799,
157353,
15072,
133,
2480,
76,
54969,
8353,
304,
910,
6492,
85,
997,
114654,
1328,
441,
617,
313,
53697,
13579,
35839,
10541,
232... | [
0.08575439453125,
0.15673828125,
0.03277587890625,
0.06121826171875,
0.10986328125,
0.12744140625,
0.0322265625,
0.1212158203125,
0.1156005859375,
0.0850830078125,
0.130126953125,
0.0079345703125,
0.10174560546875,
0.1373291015625,
0.137939453125,
0.09515380859375,
0.17529296875,
0... |
8a91687e3526d1c5cf625c5e99d5da1a03d84b20 | subsection | 5 | 11 | Modified gravity on the brane | In this section we consider the fluid - Einstein or modified
fluid - on the brane y=0. We shall derive how the Hubble
parameter H varies with time t, leading eventually to the Big
Rip.We adopt the following 4D gravity model:S=\frac{1}{2\kappa _4^2} \int d^4 x \sqrt{-g}\,(f_0R^\alpha +L_m),where f_0 and \alpha are const... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 466,
"openalex_id": "",
"raw": "M. C. B. Abdalla, S. Nojiri and S. D. Odintsov, Class. Quant. Grav. 22, L35 (2005).",
"source_ref_id": "8005381b7d58696e9fdbfa08734f693f17b156c7",
"start": 400
},
{
"arxiv_... | 10.1140/epjc/s10052-008-0678-3 | 0807.1797 | Viscous Modified Gravity on a RS Brane Embedded in AdS5 | [
"Iver Brevik"
] | [
"gr-qc"
] | 2,008 | en | Physics | [
40059,
16916,
79552,
119225,
707,
73197,
297,
98,
1620,
86,
113,
145407,
35299,
122,
5844,
3642,
53465,
2661,
171859,
572,
41110,
678,
1733,
808,
4,
105207,
155605,
47,
70,
14195,
6,
93986,
30666,
25632,
201,
397,
64002,
939,
3299,
294,
... | [
0.06451416015625,
0.086669921875,
0.285888671875,
0.263427734375,
0.0054931640625,
0.2069091796875,
0.0623779296875,
0.06988525390625,
0.1759033203125,
0.1712646484375,
0.0679931640625,
0.1884765625,
0.004608154296875,
0.022247314453125,
0.0274658203125,
0.00958251953125,
0.172485351... |
c1806b5a7ac4fb1ca428146351195af87996051c | subsection | 6 | 11 | Modified gravity on the brane | Observing that R_{00}=-3\ddot{a}/a,\, R=6(\dot{H}+2H^2), as
well as T_{00}=\rho , we obtain\frac{1}{2}f_0 R^\alpha -3\alpha f_0(\dot{H}+H^2)R^{\alpha -1}
+3\alpha (\alpha -1)f_0 HR^{\alpha -2}\dot{R}=\kappa _4^2\,\rho .An important property of Eq. (REF ) is that the covariant
divergence of the LHS is equal to zero ,\na... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 375,
"openalex_id": "",
"raw": "T. Koivisto, Class. Quant. Grav. 23, 4289 (2006).",
"source_ref_id": "bd39bb66ceeb4eb778f20fe0479b1e81c40d46db",
"start": 220
}
]
} | 10.1140/epjc/s10052-008-0678-3 | 0807.1797 | Viscous Modified Gravity on a RS Brane Embedded in AdS5 | [
"Iver Brevik"
] | [
"gr-qc"
] | 2,008 | en | Physics | [
3545,
62016,
627,
7049,
8316,
15464,
11,
8152,
64,
4,
910,
41872,
841,
54651,
8353,
10461,
237,
384,
1369,
497,
6,
642,
113054,
132076,
418,
304,
420,
2389,
289,
14612,
20,
363,
1238,
132,
1328,
1052,
24854,
68940,
85398,
15,
454,
224... | [
0.012451171875,
0.0765380859375,
0.1370849609375,
0.16455078125,
0.1402587890625,
0.137451171875,
0.04681396484375,
0.0069580078125,
0.045745849609375,
0.006591796875,
0.1297607421875,
0.0064697265625,
0.1505126953125,
0.06060791015625,
0.0185394287109375,
0.109130859375,
0.013671875... |
91827c425875934dc793557b6e97dd2230d30be0 | subsection | 7 | 11 | Einstein's gravity fluid | As mentioned above, this case corresponds to f_0=1,\, \alpha =1.
As for the bulk viscosity, we shall take \zeta to be
proportional to the scalar expansion \theta =3H through a
proportionality constant, here called \tau _E,\zeta =\tau _E\theta =3\tau _E H.This form is of particular physical interest. Namely, as shown in... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 753,
"openalex_id": "",
"raw": "I. Brevik and O. Gorbunova, Gen. Rel. Grav. 37, 2039 (2005).",
"source_ref_id": "763e00870593e9393adeaa4a6e902c1732f3bd30",
"start": 302
}
]
} | 10.1140/epjc/s10052-008-0678-3 | 0807.1797 | Viscous Modified Gravity on a RS Brane Embedded in AdS5 | [
"Iver Brevik"
] | [
"gr-qc"
] | 2,008 | en | Physics | [
903,
7225,
42518,
1238,
454,
2389,
33000,
289,
14612,
11876,
92,
4498,
7840,
2481,
5646,
731,
102,
123875,
146232,
42,
14700,
66,
6889,
2347,
76067,
841,
8305,
134393,
53697,
50104,
647,
572,
3173,
72761,
33946,
21334,
40407,
35431,
1861,
... | [
0.0144500732421875,
0.08465576171875,
0.124755859375,
0.1380615234375,
0.02825927734375,
0.1270751953125,
0.11572265625,
0.09033203125,
0.2147216796875,
0.1854248046875,
0.10986328125,
0.2392578125,
0.2296142578125,
0.131103515625,
0.02197265625,
0.1544189453125,
0.187255859375,
0.... |
940cadb3ff00e4c4e5a46be15cd9d0776d534fbc | subsection | 8 | 11 | Modified gravity fluid | Assume now that f_0 and \alpha are arbitrary. Let the bulk
viscosity for the modified fluid be denoted by \zeta _\alpha . As
in Refs. , we model \zeta _\alpha by
setting it proportional to the (2\alpha -1)'th power of the
scalar expansion:\zeta _\alpha =\tau _\alpha \theta ^{2\alpha -1}=\tau _\alpha (3H)^{2\alpha -1}.T... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 322,
"openalex_id": "",
"raw": "I. Brevik, Int. J. Mod. Phys. D 15, 767 (2006).",
"source_ref_id": "93085e732968f6f1d752c13f0c424bc416c8ae05",
"start": 123
},
{
"arxiv_id": "",
"doi": "",
"end... | 10.1140/epjc/s10052-008-0678-3 | 0807.1797 | Viscous Modified Gravity on a RS Brane Embedded in AdS5 | [
"Iver Brevik"
] | [
"gr-qc"
] | 2,008 | en | Physics | [
66596,
5036,
1238,
454,
2389,
136,
6,
289,
14612,
61799,
1294,
11876,
92,
4498,
7840,
2481,
70,
73197,
297,
79552,
8,
157,
3674,
731,
102,
101,
53295,
642,
3299,
53550,
123875,
47,
4700,
110218,
927,
14537,
111,
146232,
42,
14700,
66,
... | [
0.0880126953125,
0.024078369140625,
0.0936279296875,
0.0139923095703125,
0.133056640625,
0.01885986328125,
0.012664794921875,
0.128173828125,
0.2491455078125,
0.16943359375,
0.11767578125,
0.1842041015625,
0.09686279296875,
0.2215576171875,
0.22314453125,
0.1151123046875,
0.042999267... |
6d8b9f78119f4067ca8ebc71f26f209351bc28b6 | subsection | 9 | 11 | Implications for the 5D theory | We are now equipped with the necessary background to see how the
modified fluid on the brane effects the 5D brane physics. Consider
first Eq. (REF ) on the brane (recall that this is a 5D, not a
4D, equation). It is natural from a physical point of view to use
the expressions for \rho (t) from the previous section as i... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1600,
"openalex_id": "",
"raw": "I. Brevik and O. Gorbunova, arXiv:0806.1399 [gr-qc]; to appear in Eur. Phys. J. C.",
"source_ref_id": "82b5b3a3390ffca916212f8d15bd596988ceeb00",
"start": 1472
}
]
} | 10.1140/epjc/s10052-008-0678-3 | 0807.1797 | Viscous Modified Gravity on a RS Brane Embedded in AdS5 | [
"Iver Brevik"
] | [
"gr-qc"
] | 2,008 | en | Physics | [
5036,
46979,
70,
63559,
76615,
1957,
3642,
73197,
297,
79552,
98,
1620,
86,
93425,
190,
397,
34053,
27744,
7,
137399,
5117,
864,
11766,
919,
1388,
107,
85763,
450,
4,
959,
201,
28,
5490,
2320,
83,
6083,
1295,
10,
72761,
6275,
111,
214... | [
0.0185394287109375,
0.061431884765625,
0.0260772705078125,
0.058380126953125,
0.1151123046875,
0.0171966552734375,
0.021728515625,
0.2305908203125,
0.0931396484375,
0.2666015625,
0.04644775390625,
0.2095947265625,
0.166259765625,
0.1839599609375,
0.1776123046875,
0.1689453125,
0.1195... |
96600d073c86b0d044b7fab178fcdb133867f0f3 | subsection | 10 | 11 | Implications for the 5D theory | And this brings us to the following
important conclusion: The Big Rip divergence on the brane, present
as we have seen when \alpha >1/2, becomes transferred into the
bulk. The bulk scale factor a(t,y) diverges for arbitrary y at
t=t_s, if a_0(t) diverges at t_s. This result could hardly
have been seen beforehand, witho... | {
"cite_spans": []
} | 10.1140/epjc/s10052-008-0678-3 | 0807.1797 | Viscous Modified Gravity on a RS Brane Embedded in AdS5 | [
"Iver Brevik"
] | [
"gr-qc"
] | 2,008 | en | Physics | [
903,
19095,
1821,
25632,
5526,
93192,
14195,
6,
93986,
45,
814,
110343,
98,
70,
1620,
86,
13379,
51592,
3229,
289,
14612,
977,
118551,
24209,
12302,
2822,
3934,
11876,
92,
105994,
31461,
10,
18,
4,
53,
74789,
100,
61799,
113,
99,
808,
... | [
0.0207977294921875,
0.0203704833984375,
0.002593994140625,
0.050506591796875,
0.1109619140625,
0.134033203125,
0.1417236328125,
0.00848388671875,
0.261474609375,
0.1312255859375,
0.216552734375,
0.1683349609375,
0.07403564453125,
0.031524658203125,
0.2099609375,
0.199951171875,
0.048... |
0666fc703c627e44ce30611e0d4ddb136d4344c8 | abstract | 0 | 23 | Abstract | We report a way of wave function estimation for the density matrix
renormalization group (DMRG) method applied to quantum systems, which has
2-site modulation, when the system size extension is necessary in both the
finite and the infinite algorithms. The estimation is performed by
renormalization group (RG) transforma... | {
"cite_spans": []
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
13416,
3917,
259,
272,
32354,
25902,
1363,
168,
7,
50944,
425,
456,
33176,
47691,
21115,
31246,
48802,
55300,
190659,
47,
110436,
76519,
4,
4720,
11090,
17055,
2320,
70,
5426,
13267,
111938,
83,
63559,
23,
94418,
13,
54241,
234873,
51339,
... | [
0.07281494140625,
0.1202392578125,
0.1778564453125,
0.1446533203125,
0.230712890625,
0.205810546875,
0.075439453125,
0.169921875,
0.0501708984375,
0.1522216796875,
0.072509765625,
0.1182861328125,
0.19921875,
0.0958251953125,
0.1845703125,
0.1092529296875,
0.272705078125,
0.1776123... |
adb6a0ad9936ed2722ac539496e8c72823e57042 | subsection | 1 | 23 | Introduction | Variational estimation of minimum eigenvalues of quantum Hamiltonians and
maximum eigenvalues of classical transfer matrices has been investigated as a
non perturbative way of analysis in condensed matter systems. The Kramers-Wannier
approximation applied to the two-dimensional (2D) Ising model is one of
the early exam... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 598,
"openalex_id": "",
"raw": "H.A. Kramers and G.H. Wannier: Phys. Rev. 60 (1941) 263.",
"source_ref_id": "42da03013b5f8cf42cabaffca6113d1def7b847d",
"start": 214
},
{
"arxiv_id": "",
"doi": "",
... | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
111477,
43315,
25902,
15440,
8518,
27494,
90,
111,
110436,
94674,
72004,
136,
38132,
54704,
289,
12302,
50944,
5170,
2809,
32603,
3674,
237,
10,
351,
170950,
4935,
3917,
114137,
23,
158,
555,
5281,
26866,
76519,
80999,
1314,
1456,
47141,
56... | [
0.27294921875,
0.13134765625,
0.221435546875,
0.181884765625,
0.180908203125,
0.173828125,
0.02239990234375,
0.0228271484375,
0.1585693359375,
0.16748046875,
0.10321044921875,
0.03411865234375,
0.13037109375,
0.11669921875,
0.0226898193359375,
0.16943359375,
0.1868896484375,
0.0030... |
9a8c9f64b2bf56fb688a2602b480acba84f0b706 | subsection | 2 | 23 | Matrix Product Formulation | Consider the eigenvalue problem for the ground state of a 1D quantum system
that has modulation of period 2. An example of such systems is the dimerized S = 1/2
Heisenberg spin chain of length 2N, which is defined by the HamiltonianH^{( 2N )}_{~} = J \sum _{i = 1}^{2N - 1} \left\lbrace 1 + \delta ( - 1 )^i_{~} \right\r... | {
"cite_spans": []
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
137399,
8518,
27494,
13,
2967,
61585,
11341,
106,
397,
110436,
5426,
1556,
17055,
2320,
14922,
787,
27781,
76519,
45,
1991,
29367,
159,
22128,
19614,
48467,
25927,
121293,
140909,
116,
839,
61924,
94674,
3378,
841,
821,
11832,
304,
997,
174... | [
0.0736083984375,
0.2255859375,
0.2374267578125,
0.0474853515625,
0.197509765625,
0.2578125,
0.198974609375,
0.0445556640625,
0.0667724609375,
0.129638671875,
0.185791015625,
0.0176239013671875,
0.1778564453125,
0.039154052734375,
0.1932373046875,
0.11669921875,
0.1400146484375,
0.1... |
e865e652d803f1b4d091ff14b44c3929acd68240 | subsection | 3 | 23 | Matrix Product Formulation | The density matrices for the both sides of the system\rho ^{\rm L}_{~}( \sigma ^{\prime }_1 \sigma ^{\prime }_2 | \sigma _1^{~} \sigma _2^{~} )
\!\!\!\!\! &=& \!\!\!\!\!
\sum _{\bar{\sigma }^{~}_1 \bar{\sigma }^{~}_2}^{~}
\Psi ^{(4)}_{~}( \sigma ^{\prime }_1 \sigma ^{\prime }_2 \, \bar{\sigma }^{~}_2 \, \bar{\sigma }^{... | {
"cite_spans": []
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
581,
168,
7,
2481,
50944,
5170,
100,
70,
15044,
5609,
111,
5426,
41872,
497,
39,
339,
8152,
2306,
20561,
192,
24854,
114654,
51912,
115187,
6,
304,
58745,
101,
418,
1388,
38,
619,
1230,
11832,
1299,
8353,
454,
683,
172,
99217,
132,
13... | [
0.0869140625,
0.25830078125,
0.166748046875,
0.189453125,
0.24365234375,
0.1597900390625,
0.11279296875,
0.07318115234375,
0.203125,
0.2108154296875,
0.038421630859375,
0.246337890625,
0.031829833984375,
0.1746826171875,
0.016632080078125,
0.143798828125,
0.01605224609375,
0.071655... |
3a458d1b2424d36e2f9cf8a10df947f898f658a9 | subsection | 4 | 23 | Matrix Product Formulation | \sum _{\bar{\xi }_2^{~}}^{~} \lambda ( \bar{\xi }_2^{~} )
B_2^{~}( \bar{\sigma }^{\prime }_1 \bar{\sigma }^{\prime }_2 | \bar{\xi }_2^{~} )
B_2^{~}( \bar{\sigma }^{~}_1 \bar{\sigma }^{~}_2 | \bar{\xi }_2^{~} ) \, ,
\\where A_2^{~}( \sigma _1^{~} \sigma _2^{~} | \xi _2^{~} ) and
B_2^{~}( \bar{\sigma }^{~}_1 \bar{\sigma ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 993,
"openalex_id": "",
"raw": "I. McClloch: arXiv: 0804.2509.",
"source_ref_id": "9b8873acf1763002f2ddab73adbe41c7b55f0cbe",
"start": 632
}
]
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
41872,
11832,
101,
1299,
5134,
51912,
304,
8353,
24854,
2306,
47391,
8152,
6,
143,
6492,
85,
15,
454,
1388,
335,
132,
20561,
192,
114654,
115187,
58745,
4,
136913,
62,
418,
136,
621,
707,
24948,
6126,
289,
50944,
5170,
107013,
538,
3363... | [
0.059906005859375,
0.2474365234375,
0.0292205810546875,
0.1395263671875,
0.2252197265625,
0.011871337890625,
0.1429443359375,
0.01202392578125,
0.012054443359375,
0.1363525390625,
0.006103515625,
0.011993408203125,
0.021636962890625,
0.109619140625,
0.2467041015625,
0.18798828125,
0.... |
81f1e1e8e296baa43623d51940b5628491590435 | subsection | 5 | 23 | Matrix Product Formulation | It is possible to make
\Lambda _2^{~} diagonal by applying singular value decomposition (SVD)
directly to \Psi ^{(4)}_{~},
but we do not assume the diagonal property of the center matrices in the following.
Using the obtained matrices, we can write
\Psi ^{(4)}_{~} in the form of matrix product&&\Psi ^{(4)}_{~}( \sigma ... | {
"cite_spans": []
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
83,
7722,
47,
3249,
41872,
2729,
6492,
85,
101,
304,
8353,
2306,
207997,
390,
59911,
214,
67824,
34292,
8,
277,
40322,
43486,
397,
16,
105237,
6,
683,
172,
99217,
8152,
24854,
959,
57266,
27585,
50944,
5170,
70,
25632,
113054,
297,
4,
... | [
0.010284423828125,
0.15087890625,
0.0226593017578125,
0.147216796875,
0.04315185546875,
0.0751953125,
0.192626953125,
0.134521484375,
0.048828125,
0.1920166015625,
0.083984375,
0.15673828125,
0.29833984375,
0.02313232421875,
0.1165771484375,
0.008148193359375,
0.2261962890625,
0.16... |
cf90111a81cab2e24e8f4753367fa745b5183e6f | subsection | 6 | 23 | Matrix Product Formulation | (2.3)-(2.6), we obtain the
matrix product expression&&{\tilde{\Psi }}^{(6)}_{~}( \xi _2^{~} \, \sigma _3^{~} \, \bar{\sigma }_3^{~} \, \bar{\xi }_2^{~} )
\\
&&= \sum _{\xi _3^{~} \bar{\xi }_3^{~}}^{~}
A_3^{~}( \xi _2^{~} \sigma _3^{~} | \xi _3^{~} )
\Lambda _3^{~}( \xi _3^{~} | \bar{\xi }_3^{~} )
B_3^{~}( \bar{\xi }^{~... | {
"cite_spans": []
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
120883,
154784,
642,
113054,
50944,
425,
12996,
125195,
3675,
112,
24854,
683,
172,
8353,
169073,
8152,
454,
132,
5134,
304,
2306,
6,
41872,
4,
20561,
192,
363,
1299,
51912,
1388,
18991,
619,
1230,
1369,
11832,
101,
47391,
62,
58745,
6492... | [
0.1854248046875,
0.229736328125,
0.0146636962890625,
0.0865478515625,
0.1895751953125,
0.1097412109375,
0.267822265625,
0.21435546875,
0.0831298828125,
0.118896484375,
0.0054931640625,
0.007232666015625,
0.1092529296875,
0.00543212890625,
0.0986328125,
0.00543212890625,
0.00546264648... |
82008f16fd00448e8cb7bd02b15452c4d9178d77 | subsection | 7 | 23 | Matrix Product Formulation | \delta ( \sigma _1^{~} | \xi _1^{~} ) \\
B_1^{~}( \bar{\xi }_0^{~} \bar{\sigma }_1^{~} | \bar{\xi }_1^{~} ) \!\!\!\! &=& \!\!\!\!
\delta ( \bar{\sigma }_1^{~} | \bar{\xi }_1^{~} ) \, ,where \delta ( a | b ) represents Kronecker's delta \delta _{ab}^{~}.
With the help of these boundary orthogonal matrices, we can expres... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1293,
"openalex_id": "",
"raw": "T. Nishino, T. Hikihara, K. Okunishi, and Y. Hieida: Int. J. Mod. Phys. B 13 (1999) 1.",
"source_ref_id": "961d4e3d482da92ac693850c6d532db8827e0b7f",
"start": 1134
}
]
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
41872,
1743,
102,
15,
6,
20561,
192,
418,
24854,
2306,
8152,
5134,
1388,
335,
115187,
132,
1299,
51912,
454,
2389,
8353,
38,
619,
1369,
1230,
58745,
4,
10,
876,
33636,
7,
63325,
13,
11050,
25,
40703,
2055,
70,
4358,
111,
99091,
707,
... | [
0.07342529296875,
0.1910400390625,
0.2110595703125,
0.0140838623046875,
0.006256103515625,
0.14697265625,
0.097412109375,
0.012725830078125,
0.006683349609375,
0.03143310546875,
0.006744384765625,
0.135986328125,
0.006134033203125,
0.09381103515625,
0.10107421875,
0.00555419921875,
0... |
e6dbc1df06296d03485ee4171fbbdc18d976e321 | subsection | 8 | 23 | Matrix Product Formulation | A_1^{~} A_2^{~} \ldots A_{N-1}^{~}
{\tilde{\Psi }}^{(2N)}_{~}
B_{N-1}^{\dagger } \ldots B_2^{\dagger } B_1^{\dagger }
\, ,where configuration sum is taken for all the block spin variables,
and where {\tilde{\Psi }}^{(2N)}_{~} = A_N^{~} \Lambda _N^{~} B_N^{\dagger }.
Figure 1 shows the graphical representation of \Psi ^... | {
"cite_spans": []
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
62,
115187,
8353,
2306,
454,
304,
24854,
8152,
6,
30591,
839,
5759,
3675,
112,
683,
172,
47391,
54753,
16,
335,
85,
21407,
51912,
41872,
4,
180346,
10554,
83,
100,
756,
46389,
25927,
77336,
7,
136,
2203,
6492,
55412,
13,
106,
70,
4846... | [
0.112548828125,
0.0760498046875,
0.010833740234375,
0.0528564453125,
0.0078125,
0.061004638671875,
0.008697509765625,
0.00848388671875,
0.007568359375,
0.045166015625,
0.1357421875,
0.156494140625,
0.1800537109375,
0.2100830078125,
0.0478515625,
0.126708984375,
0.0086669921875,
0.0... |
efe5dbc59642c90fe77bbf8a0b3295cb26a8a300 | subsection | 9 | 23 | Matrix Product Formulation | A_{N-1}^{\dagger } \ldots A_{1}^{\dagger } \Psi ^{(2N)}_{~} B_{1}^{~} \ldots B_{N-1}^{~} \, ,where we have identified the wave function \Psi ^{(2N)}_{~} as a 3-leg tensor,
which has (dummy) matrix indices \xi _0^{~} and \bar{\xi }_0^{~} in addition to the
row spin variables \lbrace \sigma \rbrace = \sigma _1^{~} \ldots... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 391,
"openalex_id": "",
"raw": "It is possible to choose the case 2N = 0 or 2N = 2 as the starting point of DMRG calculation, where the choice is interesting from the computational view point.",
"source_ref_id": "fb64524e2c1... | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
62,
839,
5759,
85,
21407,
7344,
30591,
418,
683,
172,
54753,
2306,
335,
136913,
207487,
259,
272,
32354,
237,
10,
5691,
2828,
1492,
4970,
1556,
10863,
1176,
50944,
425,
136044,
5134,
2389,
1299,
66044,
15555,
25927,
77336,
99407,
20561,
1... | [
0.152587890625,
0.1749267578125,
0.232421875,
0.0865478515625,
0.235595703125,
0.00701904296875,
0.0777587890625,
0.07275390625,
0.1112060546875,
0.2178955078125,
0.130615234375,
0.024688720703125,
0.1524658203125,
0.013336181640625,
0.14111328125,
0.1689453125,
0.146484375,
0.1690... |
0815c5344a1ea49e9d076c0cd95bc59c3f11a0dd | subsection | 10 | 23 | Wave Function Renormalization | Suppose we have matrix product expressions for
\Psi ^{(4)}_{~} and \Psi ^{(6)}_{~} in Eq. (2.9), and need to obtain that of
\Psi ^{(8)}_{~}. This need is fulfilled if we diagonalize the Hamiltonian H^{(8)}_{~} via eigen solver such as the Lanczos
method. Under the situation it is important to prepare
a good trial (or i... | {
"cite_spans": []
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
121691,
8364,
642,
765,
50944,
425,
12996,
125195,
7,
41872,
683,
172,
13331,
24854,
99217,
8152,
454,
2306,
136,
6,
169073,
23,
241,
864,
5,
1126,
247,
3871,
47,
113054,
450,
111,
50490,
211394,
297,
2174,
207997,
20650,
94674,
3378,
5... | [
0.07635498046875,
0.045623779296875,
0.0159912109375,
0.0518798828125,
0.1546630859375,
0.0833740234375,
0.2254638671875,
0.2200927734375,
0.0899658203125,
0.0255279541015625,
0.1141357421875,
0.18212890625,
0.037322998046875,
0.025604248046875,
0.1561279296875,
0.025543212890625,
0.... |
f99f02af7ce047407899d3d7277042fe3a8a5545 | subsection | 11 | 23 | Wave Function Renormalization | \sum _{\sigma _1^{~} \sigma _2^{~} \sigma _3^{~} \bar{\sigma }_3^{~} \bar{\sigma }_2^{~}
\bar{\sigma }_1^{~}}^{~} \!\!\!\!
A_3^{\dagger } A_2^{\dagger } A_1^{\dagger } \, \Psi _{\rm trial}^{(8)} \,
B_1^{~} B_2^{~} B_3^{~}as we have done in Eq. (2.11).
Figure 2 shows the graphical representation of the above wave functi... | {
"cite_spans": []
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
41872,
11832,
101,
20561,
192,
418,
2306,
8152,
304,
6,
363,
1299,
51912,
454,
24854,
115187,
8353,
47391,
38,
62,
85,
21407,
683,
172,
42,
39,
110324,
50490,
335,
162,
642,
765,
16940,
864,
48105,
55412,
13,
116,
45831,
48461,
289,
1... | [
0.0167236328125,
0.2178955078125,
0.0142822265625,
0.1845703125,
0.1351318359375,
0.031005859375,
0.0750732421875,
0.018646240234375,
0.05694580078125,
0.015869140625,
0.103759765625,
0.12109375,
0.0171966552734375,
0.017669677734375,
0.0176849365234375,
0.08197021484375,
0.017654418... |
9bf3ffae2aaa21ae810530153c456abe968fa894 | subsection | 12 | 23 | Wave Function Renormalization | (3.1) can be written as\Psi _{\rm trial}^{(8)}
&=&
A_{-1}^{~} A_0^{~} A_1^{~} A_2^{~} \Lambda _2^{~}
B_2^{\dagger } B_1^{\dagger } B_0^{\dagger } B_{-1}^{\dagger } \\
&=&
A_{-1}^{~} A_0^{~} A_1^{~} {\tilde{\Psi }}^{(4)}_{~}
B_1^{\dagger } B_0^{\dagger } B_{-1}^{\dagger } \, ,where {\tilde{\Psi }}^{(4)}_{~}( \xi _1^{~} ... | {
"cite_spans": []
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
97109,
16,
831,
186,
59121,
237,
41872,
683,
172,
101,
42,
39,
110324,
8152,
8353,
24854,
50490,
619,
1369,
1230,
62,
454,
5759,
2306,
2389,
115187,
304,
6,
6492,
85,
335,
21407,
51912,
18991,
10666,
3675,
112,
47391,
99217,
4,
136913,
... | [
0.248291015625,
0.050811767578125,
0.1295166015625,
0.0157470703125,
0.200927734375,
0.0947265625,
0.0162811279296875,
0.1109619140625,
0.197998046875,
0.01617431640625,
0.045654296875,
0.09765625,
0.29150390625,
0.0374755859375,
0.0180206298828125,
0.0165252685546875,
0.242431640625... |
e3bba17a0d1e080573debd1b7d73915b81fb6b27 | subsection | 13 | 23 | Wave Function Renormalization | A_3^{\dagger } A_2^{\dagger } A_1^{\dagger }
A_{-1}^{~} A_0^{~} A_1^{~} {\tilde{\Psi }}^{(4)}_{~}
B_1^{\dagger } B_0^{\dagger } B_{-1}^{\dagger }
B_1^{~} B_2^{~} B_3^{~} \\
&=& \sum _{\xi ^{~}_1 \bar{\xi }^{~}_1}^{~}
L_3^{~}( \xi _3^{~} | \xi ^{~}_1 ) \,
{\Psi }^{(4)}_{~}( \xi ^{~}_1 \sigma _4^{~} \, \bar{\sigma }_4^{~... | {
"cite_spans": []
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
62,
454,
363,
8353,
24854,
41872,
85,
21407,
51912,
304,
115187,
5759,
8152,
2306,
2389,
3675,
112,
683,
172,
6,
99217,
335,
18991,
619,
1369,
1230,
11832,
5134,
1299,
339,
132,
101,
58745,
13331,
1388,
4,
10666,
20561,
192,
617,
627,
... | [
0.1822509765625,
0.05926513671875,
0.2279052734375,
0.1463623046875,
0.041259765625,
0.05859375,
0.15869140625,
0.258544921875,
0.05621337890625,
0.1248779296875,
0.20947265625,
0.1627197265625,
0.039154052734375,
0.1558837890625,
0.122802734375,
0.222412109375,
0.21826171875,
0.04... |
f0a4c0ee0a0e3f6652a0c4653f625fd13ab8f1ef | subsection | 14 | 23 | Wave Function Renormalization | \sum _{\bar{\sigma }_1^{~} \bar{\sigma }_2^{~} \bar{\sigma }_3^{~} \xi _2^{~}}^{~}
B_2^{~}( \bar{\sigma }_1^{~} \bar{\sigma }_2^{~} | \bar{\xi }_2^{~} ) \,
B_3^{~}( \bar{\xi }_2^{~} \bar{\sigma }_3^{~} | \bar{\xi }_3^{~} )
B_1^{~}( \bar{\xi }_1^{~} \bar{\sigma }_1^{~} | \bar{\xi }_1^{~} )Figure 3 shows the graphical re... | {
"cite_spans": []
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
41872,
11832,
1299,
20561,
192,
115187,
8353,
24854,
2306,
8152,
6,
51912,
454,
304,
363,
5134,
47391,
335,
132,
58745,
1388,
4,
6795,
138,
45831,
70,
48461,
289,
18811,
1363,
339,
136,
627,
50944,
5170,
765,
10,
32354,
111,
9473,
712,
... | [
0.029815673828125,
0.23486328125,
0.114501953125,
0.16845703125,
0.1329345703125,
0.069091796875,
0.029754638671875,
0.02984619140625,
0.1121826171875,
0.029876708984375,
0.029815673828125,
0.029754638671875,
0.0297393798828125,
0.06939697265625,
0.10296630859375,
0.179931640625,
0.0... |
c771e38434091b1dd417d7574556e445e2dc736b | subsection | 15 | 23 | Wave Function Renormalization | \sum _{\xi _2^{~} \bar{\xi }_2^{~}}^{~}
L_4^{~}( \xi _4^{~} | \xi _2^{~} ) {\tilde{\Psi }}^{(6)}_{~}( \xi _2^{~} \sigma _5^{~} \, \bar{\sigma }_5^{~} \,
\bar{\xi }_2^{~} ) R_4^{~}( \bar{\xi }_4^{~} | \bar{\xi }_2^{~} ) \, ,where L_4^{~} and R_4^{~} are defined as followsL_4^{~}( \xi _4^{~} | \xi _2^{~} ) \!\!\!\! &=& \... | {
"cite_spans": []
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
41872,
11832,
5134,
304,
8353,
24854,
2306,
8152,
6,
1299,
51912,
339,
454,
617,
58745,
1388,
10666,
3675,
112,
172,
47391,
169073,
132,
20561,
192,
758,
4,
627,
136913,
136,
61924,
71,
237,
28960,
866,
38,
619,
1369,
62,
85,
21407,
3... | [
0.0216064453125,
0.257568359375,
0.208251953125,
0.1202392578125,
0.09051513671875,
0.0548095703125,
0.15234375,
0.0215911865234375,
0.021087646484375,
0.1588134765625,
0.0209808349609375,
0.19189453125,
0.068603515625,
0.224853515625,
0.0341796875,
0.0208892822265625,
0.020004272460... |
0398be59d38e3c44fabbfab008e2bdd64d64192b | subsection | 16 | 23 | Wave Function Renormalization | The process of wave function estimation is drawn in Fig. 5.
[Figure: Construction of L_4^{~} (upper) and R_4^{~} (lower) in Eq. (3.9).][Figure: Graphical representation of the wave function estimation.]It is straight forward to extend the relation in Eqs. (3.8) and (3.9)
for arbitrary system size. This is the way of wa... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1168,
"openalex_id": "",
"raw": "T. Nishino and K. Okunishi: J. Phys. Soc. Jpn. 64 (1995) 4084.",
"source_ref_id": "2d2b45c47557f6377707bb488209e3ccdbdc8cc2",
"start": 906
},
{
"arxiv_id": "",
"doi"... | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
9433,
259,
272,
32354,
25902,
1363,
79442,
119895,
1892,
6795,
13,
195769,
339,
454,
617,
24854,
2306,
8152,
15,
34,
8079,
16,
136,
627,
8353,
17336,
56,
23,
241,
864,
5,
156611,
189682,
289,
18811,
80560,
40225,
65042,
70,
41911,
7,
... | [
0.149658203125,
0.210693359375,
0.1888427734375,
0.2437744140625,
0.2451171875,
0.1202392578125,
0.08135986328125,
0.088134765625,
0.0521240234375,
0.0325927734375,
0.0200347900390625,
0.09521484375,
0.0946044921875,
0.043731689453125,
0.101806640625,
0.02667236328125,
0.145874023437... |
751f5acb1872f5f322d2af9722502cdbf46c8a54 | subsection | 17 | 23 | Convergence to the Thermodynamic Limit | The estimated wave function&&\Psi ^{(2N+2)}_{\rm trial}( \sigma _1^{~} \ldots \sigma _{N+1}^{~} \,
\bar{\sigma }_{N+1}^{~} \ldots \bar{\sigma }_1^{~} ) \\
&&=
\Psi ^{(2N-2)}_{~}( \sigma _3^{~} \ldots \sigma _{N-1}^{~} \,
\bar{\sigma }_{N-1}^{~} \ldots \sigma _1^{~} ) \,is normally not accurate enough,
since the estimat... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1212,
"openalex_id": "",
"raw": "I. McClloch: arXiv: 0804.2509.",
"source_ref_id": "9b8873acf1763002f2ddab73adbe41c7b55f0cbe",
"start": 639
}
]
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
25902,
3674,
259,
272,
32354,
1230,
683,
172,
54753,
839,
54651,
16,
8152,
24854,
39,
110324,
6,
41872,
20561,
8353,
2306,
192,
21748,
4,
1299,
51912,
454,
7344,
30591,
1388,
18991,
1369,
13331,
10461,
132,
363,
5759,
164,
3638,
538,
95... | [
0.207763671875,
0.09808349609375,
0.1959228515625,
0.145751953125,
0.1951904296875,
0.034088134765625,
0.047119140625,
0.134765625,
0.08685302734375,
0.1036376953125,
0.252197265625,
0.0142364501953125,
0.014373779296875,
0.0142822265625,
0.012451171875,
0.19873046875,
0.014144897460... |
9ce2685c1df570d7ac696b980137c168141aea17 | subsection | 18 | 23 | Convergence to the Thermodynamic Limit | Diagonalize {\tilde{H}}^{(6)}_{~} and obtain {\tilde{\Psi }}^{(6)}_{~},
A_3^{~}, and B_3^{~}.
(c)
Contracting A_3^{~} and B_3^{~} as Eqs. (3.6) and (3.7), respectively,
to obtain L_3^{~} and R_3^{~}. Set N = 3.
(d)
Obtain {\tilde{\Psi }}^{(2N+2)}_{\rm trial} by applying L_N^{~}
and R_N^{\dagger } to {\tilde{\Psi }}^{(2... | {
"cite_spans": []
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
4512,
58108,
119066,
3675,
112,
841,
24854,
169073,
8152,
2306,
113054,
172,
47391,
8353,
454,
4,
363,
136,
335,
5,
15,
149957,
62,
237,
241,
864,
7,
102738,
16,
109981,
247,
538,
339,
627,
19943,
541,
2203,
1031,
3545,
25500,
683,
6,... | [
0.001312255859375,
0.10748291015625,
0.0721435546875,
0.1966552734375,
0.1953125,
0.101318359375,
0.002471923828125,
0.105224609375,
0.002471923828125,
0.042694091796875,
0.091064453125,
0.09521484375,
0.002899169921875,
0.002593994140625,
0.002166748046875,
0.002227783203125,
0.0750... |
de5013bfa0fa42a893683ef646c7a8045902267b | subsection | 19 | 23 | Convergence to the Thermodynamic Limit | The recursion relationL_{N+1}^{~} &=& \sum _{\sigma _{N+1}^{~}}^{~}
A_{N+1}^{\dagger } L_N^{~} A_{N-1}^{~} \\
R_{N+1}^{~} &=& \sum _{\sigma _{N+1}^{~}}^{~}
B_{N+1}^{\dagger } R_N^{~} B_{N-1}^{~}can be regarded as linear transformations to L_{N}^{~} and R_{N}^{~}, which
have their fixed points in the limit N \rightarrow... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 742,
"openalex_id": "",
"raw": "Y. Hieida, K. Okunishi and Y. Akutsu: Phys. Lett. A 233 (1997) 464.",
"source_ref_id": "ddb8888727c919c6e341f058ed61136eb49f6a4c",
"start": 533
},
{
"arxiv_id": "",
"... | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
581,
195625,
1830,
41911,
866,
839,
21748,
2306,
1230,
11832,
20561,
85,
21407,
339,
62,
5759,
627,
335,
4398,
28601,
192617,
167201,
454,
136,
2363,
188347,
26847,
17475,
541,
46632,
939,
14012,
46389,
25927,
117249,
15549,
903,
111938,
94... | [
0.0165863037109375,
0.271728515625,
0.1414794921875,
0.216552734375,
0.0843505859375,
0.1236572265625,
0.217041015625,
0.083740234375,
0.0220489501953125,
0.2130126953125,
0.142822265625,
0.00543212890625,
0.1160888671875,
0.1046142578125,
0.0682373046875,
0.1285400390625,
0.11401367... |
b831b0c3457f750413a24c0de0d99e264d13097a | subsection | 20 | 23 | Convergence to the Thermodynamic Limit | McClloch's way of wave function estimation is obtained by
decreasing the system size of this inverse matrix by 2\Phi _{\rm L}^{(2N)} \left( \Psi ^{(2N-2)}_{~} \right)^{-1}_{~} \Phi _{\rm R}^{(2N)}
= \Psi ^{(2N+2)}_{\rm trial} \, ,where we \Phi _{\rm L}^{(2N)} and \Phi _{\rm R}^{(2N)} are rectangular
matrices&&\Phi _{\r... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1028,
"openalex_id": "",
"raw": "R.J. Baxter: Exactly Solved Models in Statistical Mechanics, Academic Press, London (1982).",
"source_ref_id": "fa56c20a0f1d58f870062bf7e95259a675924c0c",
"start": 831
}
]
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
85283,
9284,
206,
25,
7,
3917,
111,
259,
272,
32354,
25902,
1363,
83,
113054,
297,
390,
8,
7612,
162,
214,
70,
5426,
13267,
903,
23,
37676,
50944,
425,
116,
45689,
14,
24854,
41872,
42,
39,
339,
8152,
8353,
54753,
839,
16,
6,
133,
... | [
0.1295166015625,
0.2039794921875,
0.22607421875,
0.0504150390625,
0.011993408203125,
0.1754150390625,
0.0214080810546875,
0.1988525390625,
0.1737060546875,
0.22998046875,
0.2410888671875,
0.1033935546875,
0.00714111328125,
0.1414794921875,
0.007598876953125,
0.023345947265625,
0.0764... |
c70cb8e84e46a504e921912de22fa4315dcf24b8 | subsection | 21 | 23 | Convergence to the Thermodynamic Limit | (4.7) we obtain\Psi _{\rm trial}^{(2N+2)} = \!\!\!\! && \!\!\!\!
{A^{\prime }}_1^{~} \ldots {A^{\prime }}_{N}^{~} {\Lambda ^{\prime }}_{N}^{~} {B^{\prime }}_{N}^{\dagger } R^{\dagger }_{~}
\left( \Lambda _{N-1}^{~} \right)^{-1}_{~} L \\
&&{A^{\prime }}_{N} {\Lambda ^{\prime }}_{N}^{~} {B^{\prime }}_{N}^{\dagger } \ldot... | {
"cite_spans": []
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
9451,
36076,
642,
113054,
41872,
683,
172,
101,
42,
39,
110324,
8152,
24854,
54753,
839,
54651,
16,
2203,
38,
1230,
6,
284,
114654,
115187,
2306,
30591,
8353,
47391,
454,
10666,
6492,
85,
571,
21407,
51912,
627,
133,
5759,
339,
18991,
1... | [
0.0655517578125,
0.137451171875,
0.0858154296875,
0.1806640625,
0.01397705078125,
0.161865234375,
0.2490234375,
0.0276336669921875,
0.04681396484375,
0.09808349609375,
0.322265625,
0.060211181640625,
0.0185546875,
0.1763916015625,
0.2227783203125,
0.330810546875,
0.012481689453125,
... |
0a51d4ad3b02a79d288e08c3fe7012756d564618 | subsection | 22 | 23 | Conclusions | We have formulated a way of applying the PWFRG method for quantum spin systems
which have 2-site modulation. In order to estimate the initial wave function, we shift the
application of renormalization group transformation to the wave function by 2 lattice cites.
As a result, we obtain a recursive relation among renorma... | {
"cite_spans": []
} | 10.1143/JPSJ.77.114002 | 0807.1798 | Two-Site shift Product Wave Function Renormalization Group Method
Applied to Quantum Systems | [
"Hiroshi Ueda",
"Tomotoshi Nishino",
"Koichi Kusakabe"
] | [
"quant-ph",
"cond-mat.stat-mech"
] | 2,008 | en | Physics | [
26168,
3917,
59911,
436,
168437,
48802,
55300,
110436,
25927,
76519,
4720,
11090,
17055,
2320,
25902,
61475,
259,
272,
32354,
122925,
38415,
456,
33176,
47691,
21115,
167201,
116,
10495,
24494,
113721,
195625,
41911,
54940,
29367,
93511,
227066,
... | [
0.10205078125,
0.1097412109375,
0.12255859375,
0.0626220703125,
0.1424560546875,
0.28271484375,
0.174072265625,
0.1571044921875,
0.21435546875,
0.1669921875,
0.12890625,
0.1988525390625,
0.1795654296875,
0.011932373046875,
0.17431640625,
0.1248779296875,
0.15478515625,
0.0958251953... |
c2612dd3ecc5d97e223ef27f3e462ccd07ccaac2 | abstract | 0 | 13 | Abstract | Scalable quantum networks require the capability to create, store and
distribute entanglement among distant nodes (atoms, trapped ions, charge and
spin qubits built on quantum dots, etc.) by means of photonic channels. We show
how the entanglement between qubits and electromagnetic field modes allows
generation of enta... | {
"cite_spans": []
} | 10.1140/epjd/e2008-00214-0 | 0807.1799 | Entanglement swapping between electromagnetic field modes and matter
qubits | [
"M. Kurpas",
"E. Zipper"
] | [
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
152653,
2886,
110436,
33120,
7,
64209,
3540,
41159,
28282,
4343,
15917,
22,
14525,
19929,
54940,
95534,
110,
988,
257,
28016,
87631,
17514,
25534,
25927,
1103,
3137,
88303,
54,
390,
26950,
16186,
6402,
86723,
7639,
17721,
136,
77556,
155116,
... | [
0.211669921875,
0.1539306640625,
0.150634765625,
0.19873046875,
0.07958984375,
0.09674072265625,
0.11083984375,
0.053955078125,
0.107666015625,
0.1375732421875,
0.1385498046875,
0.0916748046875,
0.216796875,
0.1636962890625,
0.095458984375,
0.1810302734375,
0.1300048828125,
0.07843... |
89ee9d33b483992964e5e32245672c54271e0caf | subsection | 1 | 13 | Introduction | Entanglement being a quantum correlation between various parts of a system is required for quantum information processing. The quantum logic gates with qubits interacting directly with short range interaction are not suitable for linking distant nodes.
Quantum networks should be linked with light which is the best long... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 353,
"openalex_id": "",
"raw": "M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).",
"source_ref_id": "4533177802172ff1ed629244463d4f788e85dd8f",
... | 10.1140/epjd/e2008-00214-0 | 0807.1799 | Entanglement swapping between electromagnetic field modes and matter
qubits | [
"M. Kurpas",
"E. Zipper"
] | [
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
357,
14525,
19929,
8035,
110436,
16106,
57860,
17721,
67842,
63920,
111,
5426,
56065,
100,
4677,
9433,
62775,
70836,
1103,
3137,
78974,
105237,
678,
16610,
37457,
182809,
621,
959,
202319,
3126,
95534,
110,
988,
75344,
316,
33120,
7,
5608,
... | [
0.1400146484375,
0.306640625,
0.27099609375,
0.0592041015625,
0.1619873046875,
0.1722412109375,
0.1636962890625,
0.0726318359375,
0.07489013671875,
0.1080322265625,
0.0193023681640625,
0.15869140625,
0.2012939453125,
0.0191650390625,
0.140625,
0.08251953125,
0.1390380859375,
0.1307... |
8d5b8b58bc307e1dc692fa1d707e7796f9ceae90 | subsection | 2 | 13 | Conditional entanglement of qubits | Let us consider two separate qubit-field subsystems (QR)_1 and (QR)_2 described by the Jaynes-Cummings HamiltonianH_{(QR)_i} &=&\frac{\hbar \omega _{Q_i}}{2}\sigma _z+\hbar \omega _{R_i}\left( a^{\dagger }a+\frac{1}{2}\right)- \\
&&\hbar g_i\left( a \sigma _{+}+a^{\dagger } \sigma _{-} \right)with the coupling constant... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 585,
"openalex_id": "",
"raw": "E. Zipper, M. Kurpas, J. Dajka, J. Phys.: Condens. Matter 20, 275219 (2008) .",
"source_ref_id": "631521a7ad6d56e23a298323120e5ec14ba7f0c5",
"start": 466
},
{
"arxiv_id": "... | 10.1140/epjd/e2008-00214-0 | 0807.1799 | Entanglement swapping between electromagnetic field modes and matter
qubits | [
"M. Kurpas",
"E. Zipper"
] | [
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
10842,
1821,
16916,
6626,
84797,
1103,
3137,
28394,
1614,
16751,
7,
2737,
1052,
115187,
136,
16,
304,
151552,
49191,
1444,
9,
33177,
58838,
94674,
3378,
841,
14,
8152,
619,
1369,
41872,
132076,
24854,
127,
1299,
6,
306,
2765,
47391,
20561... | [
0.010009765625,
0.00018310546875,
0.06927490234375,
0.080078125,
0.1287841796875,
0.1495361328125,
0.20556640625,
0.19677734375,
0.2314453125,
0.256591796875,
0.04876708984375,
0.0946044921875,
0.14453125,
0.110107421875,
0.0255279541015625,
0.007568359375,
0.1187744140625,
0.10900... |
11f5b04eca73aecea85a8fa84ba964c39999c90b | subsection | 3 | 13 | Conditional entanglement of qubits | The entire system at t=0 is described by the vector\vert \psi (0)\rangle =\vert \psi (0)\rangle _1\otimes \vert \psi (0)\rangle _2,where \vert \psi (0)\rangle _i describes the relevant (QR)_i subsystem.We discuss the entanglement for two different initial states:\vert \psi (0)\rangle =\vert \downarrow 0 \rangle _1 \oti... | {
"cite_spans": []
} | 10.1140/epjd/e2008-00214-0 | 0807.1799 | Entanglement swapping between electromagnetic field modes and matter
qubits | [
"M. Kurpas",
"E. Zipper"
] | [
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
581,
64194,
5426,
99,
808,
145407,
83,
151552,
390,
173,
18770,
11549,
6,
15759,
6649,
41872,
5445,
133,
418,
31,
70141,
304,
14,
98363,
7,
70,
29191,
2737,
1052,
454,
1614,
16751,
5,
45252,
22,
14525,
19929,
100,
6626,
12921,
61475,
... | [
0.0146942138671875,
0.19482421875,
0.2396240234375,
0.08331298828125,
0.120849609375,
0.2274169921875,
0.02740478515625,
0.2314453125,
0.03631591796875,
0.1995849609375,
0.216552734375,
0.1474609375,
0.009613037109375,
0.1629638671875,
0.14697265625,
0.010467529296875,
0.1640625,
0... |
912e2f50a4a58af250eafd247f0c9e86f31e04ff | subsection | 4 | 13 | Conditional entanglement of qubits | Then the resulting qubit-qubit state reads\vert QQ \rangle &=& e^{-i(\omega _{R_1} + \omega _{R_2})t}[\cos (g_1 t)\cos (g_2 t) \vert \downarrow \uparrow \rangle \\
&&+ \sin (g_1 t) \sin (g_2 t) \vert \uparrow \downarrow \rangle ].After normalization the qubit-qubit density matrix \rho _{QQ} is given by:\rho _{QQ}= \fra... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 664,
"openalex_id": "",
"raw": "F. Mintert, A. R. R. Carvalho, M. Kuś, A. Buchleitner, Phys. Rep. 415, 207 (2005).",
"source_ref_id": "1f36d1793432d3c4a67dce9d5086633dd8812748",
"start": 230
},
{
"arxiv_i... | 10.1140/epjd/e2008-00214-0 | 0807.1799 | Entanglement swapping between electromagnetic field modes and matter
qubits | [
"M. Kurpas",
"E. Zipper"
] | [
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
47009,
16750,
1103,
3137,
9,
5490,
11341,
12301,
11549,
66286,
6,
5445,
133,
1369,
1230,
28,
24854,
14,
132,
41872,
306,
2765,
101,
115187,
8152,
997,
304,
16,
18,
7840,
15,
808,
34695,
118201,
18991,
619,
1328,
1596,
177,
454,
10114,
... | [
0.0272216796875,
0.083740234375,
0.152587890625,
0.2216796875,
0.0533447265625,
0.170166015625,
0.196044921875,
0.194580078125,
0.1512451171875,
0.22607421875,
0.0188446044921875,
0.1307373046875,
0.0872802734375,
0.018798828125,
0.034393310546875,
0.06494140625,
0.0189666748046875,
... |
26e728b8c0f7d8077a5b40a8271193c7a3d3da21 | subsection | 5 | 13 | Conditional entanglement of qubits | The signature of entanglement are the non-diagonal matrix elements.
Between the probabilities P_i, i=1\div 4 and the linear entropy there exists a simple relationS_{L}=2 P_{2}P_{3}Because we are working with the J-C Hamiltonian and due to the projection onto
\vert \psi ^{-}\rangle _R state only two(\vert \downarrow \up... | {
"cite_spans": []
} | 10.1140/epjd/e2008-00214-0 | 0807.1799 | Entanglement swapping between electromagnetic field modes and matter
qubits | [
"M. Kurpas",
"E. Zipper"
] | [
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
581,
138256,
111,
22,
14525,
19929,
621,
351,
6126,
289,
50944,
425,
80854,
6300,
1177,
33,
37242,
31075,
436,
454,
14,
17,
33000,
30618,
201,
192617,
49478,
6493,
2685,
32316,
8781,
41911,
294,
866,
8152,
55257,
24854,
304,
683,
363,
2... | [
0.04815673828125,
0.293701171875,
0.11865234375,
0.133056640625,
0.28564453125,
0.2470703125,
0.05316162109375,
0.1300048828125,
0.0943603515625,
0.04168701171875,
0.15966796875,
0.07318115234375,
0.1815185546875,
0.0144805908203125,
0.06134033203125,
0.008026123046875,
0.26708984375... |
48177b8e571855cf10b78c7908509a5a320d9782 | subsection | 6 | 13 | Results | In the first part of this section we present results obtained from above formulas for coherent evolution of the QR subsystems. The influence of dissipation is discussed in the second part. The presented results are for the resonant case \omega _{Q_i} = \omega _{R_i}=\omega _R.Let us first assume g_1=g_2=g; for concrete... | {
"cite_spans": []
} | 10.1140/epjd/e2008-00214-0 | 0807.1799 | Entanglement swapping between electromagnetic field modes and matter
qubits | [
"M. Kurpas",
"E. Zipper"
] | [
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
70,
2831,
111,
40059,
13379,
50339,
113054,
297,
36917,
26168,
7,
241463,
28,
137089,
79631,
1614,
16751,
79507,
109091,
254,
2320,
45252,
17932,
8121,
71,
92526,
30125,
7225,
6,
306,
2765,
24854,
2737,
454,
14,
8152,
2203,
41872,
101,
13... | [
0.0151214599609375,
0.044769287109375,
0.0150146484375,
0.056854248046875,
0.053436279296875,
0.1114501953125,
0.044586181640625,
0.0151214599609375,
0.070068359375,
0.174560546875,
0.018829345703125,
0.2376708984375,
0.1070556640625,
0.2474365234375,
0.29345703125,
0.2025146484375,
... |
c27d2cefef19d9af44459241d154047375ce0e26 | subsection | 7 | 13 | Results | This is visible in Fig. REF for g_2=0.01. For gt=k \pi /2 the vectors \vert \Psi (t)\rangle _1 and \vert \Psi (t)\rangle _2 represent separable states and the state vector of the whole system \vert \psi (t)\rangle has no non-zero components along the direction of the Bell projector and thus the BSM is unsuccessful.Next... | {
"cite_spans": []
} | 10.1140/epjd/e2008-00214-0 | 0807.1799 | Entanglement swapping between electromagnetic field modes and matter
qubits | [
"M. Kurpas",
"E. Zipper"
] | [
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
75693,
119895,
9069,
919,
706,
454,
304,
145407,
18065,
5386,
92,
1434,
12477,
22834,
22230,
11549,
683,
172,
18,
5445,
33636,
37451,
117249,
11341,
173,
18770,
28271,
5426,
15759,
1556,
110,
351,
80510,
82761,
33233,
48225,
33500,
13452,
7... | [
0.1158447265625,
0.130859375,
0.03662109375,
0.081298828125,
0.1351318359375,
0.08740234375,
0.16455078125,
0.08123779296875,
0.116455078125,
0.1103515625,
0.058624267578125,
0.125,
0.1280517578125,
0.205322265625,
0.1424560546875,
0.158203125,
0.0177001953125,
0.0802001953125,
0... |
25e72fc47a71c9de4c381864813debc9031bd6cc | subsection | 8 | 13 | Results | Following we assume that the effect of environment can be included in terms of two independent Lindblad terms:\dot{\rho }_{QR}(t)=\left( L_H-\frac{1}{2}L_{\gamma }-\frac{1}{2}L_{\kappa }\right) \rho _{QR}(t)where the 'conservative part' is given byL_H(\cdot )=-i[H_{QR},\cdot ]whereas the 'Lindblad dissipators'L_{m}(\cd... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 599,
"openalex_id": "",
"raw": "A. Blais, R. Huang, A. Wallraff, S. M. Girvin, R. J. Schoelkopf, Phys. Rev. A 69, 062320 (2004); A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow J. Majer, L. F... | 10.1140/epjd/e2008-00214-0 | 0807.1799 | Entanglement swapping between electromagnetic field modes and matter
qubits | [
"M. Kurpas",
"E. Zipper"
] | [
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
77168,
41591,
70,
21543,
111,
65998,
831,
186,
99201,
23,
69407,
6626,
41371,
17859,
22877,
15464,
41872,
497,
51912,
454,
24854,
2737,
1052,
8152,
132,
18,
16,
1369,
133,
2480,
339,
841,
9,
132076,
418,
304,
866,
17705,
192,
161,
7495,... | [
0.07220458984375,
0.125732421875,
0.032012939453125,
0.2509765625,
0.09393310546875,
0.265869140625,
0.06890869140625,
0.047271728515625,
0.14599609375,
0.03216552734375,
0.1939697265625,
0.1190185546875,
0.10498046875,
0.1494140625,
0.252685546875,
0.067138671875,
0.032135009765625,... |
452514f0d9d6a211e1dce8e5b1340496c5eadb8e | subsection | 9 | 13 | Results | In this paper we have not considered this problem in detail, concentrating mainly on the entanglement process. However, this problem has been studied in some papers (see e.g. ).
[Figure: (color online) The qubit-qubit matrix elements at the BSM time t=0.2 \mu s for coherent evolution of QRs. The initial state \vert e0e... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 177,
"openalex_id": "",
"raw": "D. D. Bhaktavatsala Rao, V. Ravishankar, V. Subrahmanyam, Phys. Rev. A 75, 052338 (2007)",
"source_ref_id": "0ce5756e3f4c64cf5c112c29e5276b7759f6f76d",
"start": 111
}
]
} | 10.1140/epjd/e2008-00214-0 | 0807.1799 | Entanglement swapping between electromagnetic field modes and matter
qubits | [
"M. Kurpas",
"E. Zipper"
] | [
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
903,
15122,
642,
765,
959,
90698,
2967,
22443,
142156,
214,
22,
14525,
19929,
9433,
33306,
1556,
2809,
22282,
71,
23,
3060,
21231,
177,
6795,
46133,
1118,
1103,
3137,
9,
5490,
50944,
425,
80854,
99,
335,
18148,
1733,
808,
1369,
133684,
... | [
0.04632568359375,
0.1087646484375,
0.0042724609375,
0.030517578125,
0.05712890625,
0.07708740234375,
0.166015625,
0.066650390625,
0.09619140625,
0.0008544921875,
0.045196533203125,
0.22705078125,
0.1800537109375,
0.1534423828125,
0.0303955078125,
0.036773681640625,
0.005950927734375,... |
f4e9c38b112b318517f782ae6db701d350f888cf | subsection | 10 | 13 | Entanglement of spins encoded in quantum dots | Similar considerations can also be used to entangle qubits encoded in the electron spin of individual quantum dots as recently proposed in (the spin states are very long lived with relaxation times of order of milliseconds).
[Figure: Entanglement swapping procedure for photons and spins in quantum dots. The spin-photon... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 225,
"openalex_id": "",
"raw": "M. L. Leuenberger, M. E. Flatte, D. D. Awschalom, Phys. Rev. Lett.94, 107401 (2005).",
"source_ref_id": "a2dc06e8b93a8ddea5517617d64ff25d00438144",
"start": 0
},
{
"arxiv_i... | 10.1140/epjd/e2008-00214-0 | 0807.1799 | Entanglement swapping between electromagnetic field modes and matter
qubits | [
"M. Kurpas",
"E. Zipper"
] | [
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
209683,
177229,
831,
2843,
186,
11814,
47,
22,
14525,
133,
1103,
3137,
40899,
71,
23,
70,
77556,
19,
25927,
111,
11651,
110436,
54,
933,
78684,
26171,
117249,
621,
4552,
4989,
158930,
678,
20648,
2320,
20028,
12989,
8877,
191633,
7,
6159,... | [
0.10675048828125,
0.1397705078125,
0.03485107421875,
0.000640869140625,
0.0155792236328125,
0.1309814453125,
0.0224761962890625,
0.1075439453125,
0.267822265625,
0.1890869140625,
0.1368408203125,
0.2025146484375,
0.2222900390625,
0.0192413330078125,
0.035308837890625,
0.019729614257812... |
5ac77ca37fa0bc080bfaba055e86762cc4771d1a | subsection | 11 | 13 | Entanglement of spins encoded in quantum dots | The BSM on the photons outgoing from the two micro-cavities conditionally leads to entangled qubit states\vert \Psi _{QQ} \rangle &=& Tr_{ph}\left( \vert \Psi ^{-} \rangle _{phph} \langle \Psi ^{-}\vert \Psi \rangle \langle \Psi \vert \right) \\
& = &-1/ \sqrt{2}\left( \vert \uparrow \rangle _1 \vert \downarrow \rangle... | {
"cite_spans": []
} | 10.1140/epjd/e2008-00214-0 | 0807.1799 | Entanglement swapping between electromagnetic field modes and matter
qubits | [
"M. Kurpas",
"E. Zipper"
] | [
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
581,
335,
18148,
98,
16186,
1779,
1810,
519,
1295,
6626,
11948,
408,
686,
2449,
35431,
37105,
47,
22,
1076,
32502,
1103,
3137,
117249,
11549,
172,
66286,
8152,
5445,
1369,
1230,
5454,
454,
11727,
2480,
6,
24854,
127,
3066,
133,
41872,
5... | [
0.04180908203125,
0.0919189453125,
0.254638671875,
0.08624267578125,
0.177978515625,
0.1156005859375,
0.10400390625,
0.09326171875,
0.050994873046875,
0.13720703125,
0.1339111328125,
0.1015625,
0.1531982421875,
0.0823974609375,
0.1810302734375,
0.13232421875,
0.001556396484375,
0.0... |
91ee7d50b21ed7b9f0a16f60ec897e72f7459269 | subsection | 12 | 13 | Conclusions | Cavity quantum electrodynamics with individually addressable qubits (atoms, trapped ions, charge, flux or spin solid state qubits) is expected to provide a toolbox for quantum computing. The strong qubit-field coupling achievable in a high-finesse cavity can be accurately described by the Jaynes-Cummings model if g/\om... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 847,
"openalex_id": "",
"raw": "A. Blais, R. Huang, A. Wallraff, S. M. Girvin, R. J. Schoelkopf, Phys. Rev. A 69, 062320 (2004); A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow J. Majer, L. F... | 10.1140/epjd/e2008-00214-0 | 0807.1799 | Entanglement swapping between electromagnetic field modes and matter
qubits | [
"M. Kurpas",
"E. Zipper"
] | [
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
2041,
3760,
53,
110436,
77556,
242554,
678,
11651,
538,
29823,
2886,
1103,
3137,
7,
257,
28016,
4,
87631,
297,
6,
17514,
25534,
85679,
707,
25927,
18652,
11341,
16,
83,
84751,
47,
22691,
55516,
11728,
100,
242122,
37515,
28394,
14974,
206... | [
0.175537109375,
0.2418212890625,
0.08642578125,
0.1943359375,
0.137451171875,
0.2335205078125,
0.028717041015625,
0.1234130859375,
0.009033203125,
0.142578125,
0.07574462890625,
0.184814453125,
0.2255859375,
0.009246826171875,
0.0848388671875,
0.1033935546875,
0.0086669921875,
0.19... |
178568045742554511ac947328ccade5913a76e3 | abstract | 0 | 30 | Abstract | We obtain some general results on Sasakian Lie algebras and prove as a
consequence that a (2n + 1)-dimensional nilpotent Lie group admitting
left-invariant Sasakian structures is isomorphic to the real Heisenberg group
$H_{2n + 1}$. Furthermore, we classify Sasakian Lie algebras of dimension 5 and
determine which of th... | {
"cite_spans": []
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
4537,
50339,
94120,
301,
66,
29730,
144,
429,
56095,
23534,
4700,
19,
997,
157955,
17324,
114680,
21115,
36456,
25737,
73,
162591,
45646,
83,
13882,
178851,
1771,
47,
2773,
19614,
48467,
841,
304,
106,
18507,
91403,
190,
85358,
14612,
61061... | [
0.061279296875,
0.029693603515625,
0.132080078125,
0.1553955078125,
0.10443115234375,
0.1873779296875,
0.0262603759765625,
0.1099853515625,
0.1334228515625,
0.01141357421875,
0.0374755859375,
0.00653076171875,
0.108154296875,
0.1412353515625,
0.0946044921875,
0.201904296875,
0.173950... | |
14e59a1cf783daeedb7156be9fbf24c240562c60 | subsection | 1 | 30 | Introduction | A Sasakian structure is the analogous in odd dimensions of a Kähler structure. Indeed, by a Riemannian manifold (M,g) of odd dimension 2n + 1 admits a compatible Sasakian structure if and only if the Riemannian cone M\times {\mathbb {R}}^+ is Kähler.In dimension 3 a homogeneous Sasakian manifold has to be a Lie group e... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 251,
"openalex_id": "",
"raw": "Boyer C. P., Galicki K.: 3-Sasakian manifolds, Surveys in differential geometry: essays on Einstein manifolds 123–184, Surv. Differ. Geom., VI, Int. Press, Boston, MA, 1999.",
"source_ref_id":... | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
62,
94120,
301,
66,
45646,
83,
60223,
10821,
70270,
158208,
23734,
127,
603,
10,
41419,
127613,
17174,
42822,
177,
91403,
116,
19,
997,
106,
36456,
146731,
158,
13,
276,
70141,
1328,
4153,
138,
12840,
15292,
29730,
21115,
246,
25737,
73,
... | [
0.002166748046875,
0.193115234375,
0.229248046875,
0.1746826171875,
0.251708984375,
0.0224761962890625,
0.10107421875,
0.00238037109375,
0.1424560546875,
0.17578125,
0.080322265625,
0.1104736328125,
0.172607421875,
0.0059814453125,
0.0650634765625,
0.1497802734375,
0.06103515625,
0... | |
e0ab068724874ad799f0860e57d67cc206466cb9 | subsection | 2 | 30 | Introduction | Thenif {\mathfrak {g}} has non-trivial center \mathfrak {z}({\mathfrak {g}}), then {\mathfrak {g}} is solvable with \dim \mathfrak {z}({\mathfrak {g}})=1 and the quotient {\mathfrak {g}}/\mathfrak {z}({\mathfrak {g}}) carries an induced Kähler structure (see Theorem \ref {classwithcenter});
if {\mathfrak {g}} has tri... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1434,
"openalex_id": "",
"raw": "Ovando G.: Invariant pseudo-Kähler metrics in dimension four, J. Lie Theory 16 (2006), 371–391.",
"source_ref_id": "2fda1d77829a9effa2853c9a0ac5b0d61f52b1ba",
"start": 1250
},
{... | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
3190,
125458,
6000,
92,
177,
1556,
351,
3996,
686,
289,
27585,
6,
10666,
169,
8152,
132,
24854,
41872,
47391,
247,
83,
132944,
2886,
678,
5771,
16,
33000,
70,
41502,
18750,
64,
2258,
135989,
297,
23734,
127,
603,
45646,
15,
21231,
581,
... | [
0.01885986328125,
0.087158203125,
0.211181640625,
0.1959228515625,
0.15771484375,
0.051055908203125,
0.145263671875,
0.0816650390625,
0.1529541015625,
0.007171630859375,
0.18310546875,
0.007354736328125,
0.0074462890625,
0.0631103515625,
0.00738525390625,
0.007293701171875,
0.0074768... | |
c2259ac0ebde4530f9a93b3c84b71c8026eef7cc | subsection | 3 | 30 | Introduction | We show that a 5-dimensional Sasakian \alpha -Einstein Lie algebra is isomorphic either to {\mathfrak {h}}_5, {\mathfrak {g}}_0 or to {\mathfrak {sl}} (2, {\mathbb {R}}) \times {\mathfrak {aff}} ({\mathbb {R}}).Moreover, by it is known that a Lie algebra of dimension at least 5 cannot admit a Sasakian-Einstein structur... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 323,
"openalex_id": "",
"raw": "Diatta A.: Riemannian geometry on contact Lie groups, Geom. Dedicata 133 (2008), 83–94.",
"source_ref_id": "eb9e8c7415474ef63da55a10ab2a809dd32a5330",
"start": 211
}
]
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
1401,
7639,
8967,
157955,
94120,
301,
66,
14612,
61061,
18055,
29730,
144,
429,
2844,
83,
13882,
178851,
1771,
40101,
47,
125458,
6000,
92,
127,
758,
177,
2389,
707,
24861,
4700,
5125,
1052,
70141,
62566,
51529,
91403,
19713,
190,
53418,
... | [
0.00970458984375,
0.1014404296875,
0.1815185546875,
0.18994140625,
0.1492919921875,
0.1634521484375,
0.117919921875,
0.1171875,
0.10565185546875,
0.20654296875,
0.2115478515625,
0.07220458984375,
0.129150390625,
0.1502685546875,
0.0938720703125,
0.1343994140625,
0.2420654296875,
0.... | |
b8314b5d983c06f76f60e1e2ec518fa1905b3153 | subsection | 4 | 30 | Preliminaries | A triple (\Phi , \alpha , \xi ) on a (2n+1)-dimensional manifold M is an
almost contact structure if \xi is a nowhere vanishing vector field, \alpha is a
1-form, and \Phi is a tensor of type (1, 1) such that\alpha (\xi ) = 1, \quad \Phi ^2 = - {\rm I} + \xi \otimes \alpha .The vector field \xi defines the characteristi... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1999,
"openalex_id": "",
"raw": "Sasaki S., Hatakeyama Y.: On differentiable manifolds with certain structures which are closely related to almost contact structure II, Tôhoku Math. J. (2) 13 (1961), 281–294.",
"source_ref_i... | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
62,
162738,
41872,
45689,
14,
289,
14612,
5134,
98,
4700,
19,
21748,
157955,
17174,
42822,
276,
83,
142,
39555,
5470,
45646,
2174,
110,
136913,
131,
54700,
173,
18770,
44457,
4317,
5037,
1492,
4970,
10644,
4879,
6044,
106,
87,
997,
70141,... | [
0.01666259765625,
0.29638671875,
0.010772705078125,
0.192626953125,
0.1654052734375,
0.05780029296875,
0.2322998046875,
0.20556640625,
0.060150146484375,
0.07373046875,
0.0164337158203125,
0.1431884765625,
0.1439208984375,
0.07318115234375,
0.18994140625,
0.1795654296875,
0.070068359... | |
9927e0ce63a824f026e1c4df0c4e02be6c276460 | subsection | 5 | 30 | Preliminaries | Any almost contact structure admits a compatible metric.An almost contact metric structure (\Phi , \alpha , \xi , g) is said to be contact metric if2g (X, \Phi Y) = {\rm d} \alpha (X, Y)\,.In this case \alpha is a contact form and we denote\omega (X, Y) = g (X, \Phi Y).Definition 2.1
A Sasakian structure is a normal c... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 497,
"openalex_id": "",
"raw": "Sasaki S.: On differentiable manifolds with certain structures which are closely related to almost contact structure, Tôhoku Math. J. 2 (1960), 459–476.",
"source_ref_id": "acbd3444dc41412a837... | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
28541,
39555,
5470,
45646,
36456,
146731,
186518,
45689,
14,
14612,
5134,
706,
2804,
186,
2174,
304,
177,
1542,
990,
104,
3173,
48345,
306,
2765,
187423,
943,
34513,
62,
94120,
301,
66,
83,
3638,
839,
116,
62816,
41419,
127613,
158,
645,
... | [
0.07843017578125,
0.2159423828125,
0.23681640625,
0.282470703125,
0.176513671875,
0.2120361328125,
0.25439453125,
0.1573486328125,
0.12060546875,
0.22265625,
0.1593017578125,
0.16259765625,
0.0826416015625,
0.061981201171875,
0.018035888671875,
0.033416748046875,
0.1187744140625,
0... | |
588f43c5dab5e4c16f8ac12ef2f97bd4034973f6 | subsection | 6 | 30 | Preliminaries | Finally, we recall that a 5-dimensional manifold is Sasakian \alpha -Einstein if and only if it is Sasakian-hypo (see ). | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 120,
"openalex_id": "",
"raw": "Conti D., Salamon S.: Generalized Killing spinors in dimension 5, Trans. Amer. Math. Soc. 359 (2007), 5319–5343.",
"source_ref_id": "002ce858574ddf3f564f1b7b55133df31837b8e4",
"start": 0... | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
201106,
642,
189232,
8967,
157955,
17174,
42822,
83,
94120,
301,
66,
6,
41872,
14612,
61061,
18055,
2174,
4734,
3038,
771
] | [
0.054351806640625,
0.007904052734375,
0.1270751953125,
0.16943359375,
0.1702880859375,
0.09521484375,
0.193115234375,
0.06915283203125,
0.1563720703125,
0.161865234375,
0.1239013671875,
0.03564453125,
0.029266357421875,
0.1248779296875,
0.07720947265625,
0.1842041015625,
0.0343627929... | |
62d06500e6c37251a49329079e655aed4525dead | subsection | 7 | 30 | Sasakian Lie algebras | In this section we will begin our study of left-invariant Sasakian structures on Lie groups. Such a structure corresponds to a Sasakian structure on the associated Lie algebra.Definition 3.1 A Sasakian structure on a Lie algebra {\mathfrak {g}} is a quadruple (\Phi ,\alpha ,\xi ,g), where \Phi \in {\rm End}({\mathfrak ... | {
"cite_spans": []
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
903,
40059,
1221,
9842,
35187,
25737,
73,
162591,
94120,
301,
66,
45646,
7,
98,
29730,
94407,
62771,
42518,
137272,
144,
429,
2844,
187423,
943,
45151,
62,
41872,
125458,
6000,
92,
177,
47391,
83,
10,
2799,
186514,
133,
15,
45689,
14,
6... | [
0.008880615234375,
0.07452392578125,
0.013580322265625,
0.08447265625,
0.129150390625,
0.2296142578125,
0.0904541015625,
0.261474609375,
0.22265625,
0.258544921875,
0.2039794921875,
0.309326171875,
0.03375244140625,
0.076171875,
0.246337890625,
0.231201171875,
0.00653076171875,
0.0... | |
442af8012fe4487f74410798a2586118f22f424c | subsection | 8 | 30 | Sasakian Lie algebras | Then\dim {\mathfrak {z}}(\mathfrak {g})\le 1\,;
if \dim {\mathfrak {z}}(\mathfrak {g})=1, then {\mathfrak {z}}(\mathfrak {g})={\mathbb {R}}\,\xi .The first item is well known and follows from the fact that {\rm d}\alpha is non-degenerate on \ker \alpha . For the second item we
fix an arbitrary generator Z of {\mathfr... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 825,
"openalex_id": "",
"raw": "Boothby W. M., Wang H. C.: On contact manifolds, Ann. of Math. (2) 68 (1958), 721–734.",
"source_ref_id": "7df97f913f0c2e640e94a9aca74e482e35ade2ca",
"start": 674
}
]
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
47009,
5771,
6000,
92,
169,
177,
133,
106,
74,
2174,
33000,
125458,
5125,
1052,
5134,
35735,
5299,
51529,
39,
104,
289,
14612,
83,
351,
112,
48281,
67,
98,
1728,
17932,
30022,
61799,
145823,
567,
33022,
1369,
11,
997,
1542,
10,
1193,
... | [
0.012542724609375,
0.2432861328125,
0.2239990234375,
0.14794921875,
0.16015625,
0.1236572265625,
0.1226806640625,
0.086181640625,
0.001007080078125,
0.0340576171875,
0.123291015625,
0.05352783203125,
0.120361328125,
0.0919189453125,
0.246826171875,
0.1473388671875,
0.002349853515625,... | |
79b431258cf66a7fea2c46cf7169000a953c06db | subsection | 9 | 30 | Non-trivial center | We show that in the case of Sasakian Lie algebras with non-trivial center the kernel of the contact form
inherits a natural structure of Kähler Lie algebra. Moreover two Sasakian Lie algebras are isomorphic if and only if the corresponding Kähler Lie algebras are equivalent. This allows us to use the classification of ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 434,
"openalex_id": "",
"raw": "Ovando G.: Invariant pseudo-Kähler metrics in dimension four, J. Lie Theory 16 (2006), 371–391.",
"source_ref_id": "2fda1d77829a9effa2853c9a0ac5b0d61f52b1ba",
"start": 276
}
]
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
7639,
70,
7225,
94120,
301,
66,
29730,
144,
429,
56095,
678,
351,
3996,
686,
27585,
77924,
583,
5470,
3173,
23,
3334,
14481,
6083,
45646,
23734,
127,
603,
2844,
6626,
621,
13882,
178851,
136,
4734,
2174,
214,
183234,
114864,
47,
40865,
... | [
0.0869140625,
0.008148193359375,
0.0163421630859375,
0.1314697265625,
0.1744384765625,
0.0972900390625,
0.2210693359375,
0.06610107421875,
0.148193359375,
0.147216796875,
0.03240966796875,
0.135009765625,
0.08673095703125,
0.13427734375,
0.1806640625,
0.1873779296875,
0.166259765625,... | |
9ce7732e4dc8b033e81da813ffc262527bb218e1 | subsection | 10 | 30 | Non-trivial center | Then defining[X,Y]=[X,Y]_{\mathfrak {h}}-{\omega }(X,Y)\,\xifor X,Y \in \mathfrak {h} and[\xi ,\mathfrak {h}]=0we obtain a new Lie algebra ({\mathfrak {g}}, [ \, , \, ]) equipped with a natural Sasakian structure, where the contact form \alpha on {\mathfrak {g}} is defined as\alpha (a\,\xi +X)=afor all X\in \mathfrak {... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1309,
"openalex_id": "",
"raw": "Geiges H., Normal contact structures on 3-manifolds, Tôhoku Math. J. (2) 49 (1997), 415–422.",
"source_ref_id": "8b5232fa287788ff8a5bd5c00625b9d52ccf5b48",
"start": 1130
},
{
... | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
47009,
13204,
1542,
4,
1723,
268,
1369,
24854,
41872,
125458,
6000,
92,
10666,
127,
47391,
9,
306,
2765,
51912,
132,
16,
5134,
2472,
1193,
6,
73,
8152,
1065,
145407,
113054,
10,
3525,
29730,
144,
429,
2844,
177,
378,
10114,
46979,
20051... | [
0.00347900390625,
0.1549072265625,
0.14990234375,
0.047027587890625,
0.1666259765625,
0.0178375244140625,
0.037628173828125,
0.0178375244140625,
0.0178985595703125,
0.0178985595703125,
0.2205810546875,
0.1102294921875,
0.018096923828125,
0.14599609375,
0.0738525390625,
0.01771545410156... | |
b404a612e3b71e8fe8dae7bde6bf8e41b05306cf | subsection | 11 | 30 | Trivial center | In the case the Sasakian Lie algebra \mathfrak {g} has trivial center, we have the following properties for {\rm ad}_{\xi }.Proposition 3.11
Let ({\mathfrak {g}},\Phi ,\alpha ,\xi ,g) be a Sasakian Lie algebra. Then{\rm ad}_{\xi } \Phi = \Phi \,{\rm ad}_{\xi }, and therefore \ker {\rm ad}_\xi and {\rm Im}\,{\rm ad}_\x... | {
"cite_spans": []
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
7225,
94120,
301,
66,
29730,
144,
429,
2844,
6000,
92,
177,
1556,
1927,
686,
289,
27585,
25632,
183871,
39,
606,
5134,
1662,
10842,
45689,
14,
14612,
1728,
3370,
162591,
1614,
65421,
83,
230612,
706,
21177,
434,
1264,
254,
35735,
23468,
... | [
0.03350830078125,
0.152099609375,
0.19482421875,
0.0982666015625,
0.2108154296875,
0.05169677734375,
0.1163330078125,
0.133056640625,
0.1434326171875,
0.0794677734375,
0.133056640625,
0.0428466796875,
0.1070556640625,
0.1656494140625,
0.051544189453125,
0.2303466796875,
0.03765869140... | |
1804e42e95f148522ae6a507ace5c23f5295618c | subsection | 12 | 30 | Trivial center | We can write X=a\xi + \Phi X^{\prime }, with X^{\prime } \in \ker \alpha , and thus the third item follows from\begin{aligned}g([\xi , X], Y) &= g ([\xi , a \xi + \Phi X^{\prime }], Y) = g( [\xi , \Phi X^{\prime }], Y) = g (X^{\prime }, [\xi , \Phi Y])\\
&= - g(\Phi X^{\prime }, [\xi , Y]) = - g(X - a \xi , [\xi , Y]) ... | {
"cite_spans": []
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
1401,
831,
33022,
1193,
1369,
11,
5134,
997,
45689,
14,
114654,
678,
73,
1728,
289,
14612,
50960,
35735,
28960,
1295,
6820,
143420,
177,
990,
706,
10,
1542,
42,
606,
22144,
59155,
3370,
1264,
254,
157955,
1250,
40322,
9069,
919,
12116,
... | [
0.018035888671875,
0.07421875,
0.1689453125,
0.185791015625,
0.054718017578125,
0.0982666015625,
0.251220703125,
0.127685546875,
0.1119384765625,
0.08685302734375,
0.1826171875,
0.017303466796875,
0.05938720703125,
0.2197265625,
0.06201171875,
0.1968994140625,
0.193359375,
0.181762... | |
3566a4581e98f74bbf46111056e70473bc57a025 | subsection | 13 | 30 | Trivial center | Clearly \xi belongs to the
center of this subalgebra and the restrictions of \Phi and g induce a Sasakian structure on
\ker {\rm ad}_\xi .(2) We can writeX = a \xi + X^{\prime }, \quad Y = [\xi , Y^{\prime }],with a \in {\mathbb {R}}, X^{\prime } \in \ker {\rm ad}_{\xi } \cap \ker \alpha , Y^{\prime } \in {\mathfrak {g... | {
"cite_spans": []
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
86120,
41872,
5134,
186,
10617,
47,
27585,
903,
1614,
289,
429,
2844,
185190,
45689,
14,
136,
706,
135989,
94120,
301,
66,
45646,
98,
1728,
606,
40970,
1401,
831,
33022,
1542,
2203,
10,
997,
1193,
114654,
91526,
990,
15644,
14612,
6000,
... | [
0.07012939453125,
0.01385498046875,
0.249755859375,
0.02618408203125,
0.1484375,
0.1002197265625,
0.2259521484375,
0.0908203125,
0.1904296875,
0.05615234375,
0.125732421875,
0.1173095703125,
0.1912841796875,
0.10491943359375,
0.10888671875,
0.07275390625,
0.126953125,
0.15637207031... | |
a364ab3d4c3f32a13ab31e9157c092ae75dd10cb | subsection | 14 | 30 | Body | Simply connected homogeneous 3-dimensional contact metric manifolds were classified by Perrone in , showing that the homogeneous space has to be a Lie group with a left-invariant contact metric structure. Among these Lie groups we can find the ones that admit a Sasakian structure.For the sake of completeness we perform... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 204,
"openalex_id": "",
"raw": "Perrone D.: Homogeneous contact Riemannian three-manifolds, Illinois J. Math. 42 (1998), 243–256.",
"source_ref_id": "06139f857280a0ae8ee8707771711a5092c8f4ec",
"start": 0
},
{
... | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
55331,
162711,
12840,
15292,
5691,
157955,
5470,
186518,
17174,
42822,
18507,
47314,
908,
86345,
32628,
1556,
29730,
21115,
25737,
162591,
45646,
94407,
36456,
94120,
301,
66,
72018,
28484,
51339,
40865,
21771,
51529,
2206,
3112,
7,
83324,
45,
... | [
0.08929443359375,
0.169189453125,
0.1370849609375,
0.2230224609375,
0.1322021484375,
0.159423828125,
0.1556396484375,
0.1512451171875,
0.038177490234375,
0.170166015625,
0.1175537109375,
0.0625,
0.05181884765625,
0.2132568359375,
0.132080078125,
0.005859375,
0.2279052734375,
0.1678... | |
6e425a07ada316f2f80e073e1e94e4f5158506aa | subsection | 15 | 30 | Body | In the latter case there exists a basis \lbrace e^1, e^2, e^3 \rbrace
of {\mathfrak {g}}^* such that{\rm d} e^1 =0, \quad {\rm d} e^2 = e^{12}, \quad {\rm d} e^3 = 2 e^{12},with respect to which the Sasakian structure is\xi = e_3, \quad \alpha = e^3, \quad \Phi (e_1) = e_2, \quad \omega = e^{12}.Considering the new ba... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 823,
"openalex_id": "",
"raw": "Ovando G.: Invariant pseudo-Kähler metrics in dimension four, J. Lie Theory 16 (2006), 371–391.",
"source_ref_id": "2fda1d77829a9effa2853c9a0ac5b0d61f52b1ba",
"start": 651
}
]
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
21,
3055,
7225,
2685,
32316,
10,
18231,
99407,
28,
8353,
418,
304,
363,
6,
111,
41872,
6000,
92,
177,
47391,
1639,
6044,
39,
104,
8152,
145407,
4,
91526,
10666,
2203,
24854,
1530,
42,
116,
76228,
15072,
47,
70,
94120,
301,
66,
45646,
... | [
0.03167724609375,
0.0772705078125,
0.0933837890625,
0.006317138671875,
0.1380615234375,
0.0181427001953125,
0.2498779296875,
0.1285400390625,
0.09185791015625,
0.041656494140625,
0.0504150390625,
0.08740234375,
0.1318359375,
0.01434326171875,
0.0141143798828125,
0.0143890380859375,
0... | |
492e171c45e0210396c6d67b5567853e29854606 | subsection | 16 | 30 | Body | We may choose a basis \lbrace e_1, \ldots , e_5\rbrace of \mathfrak {g} such that\xi = e_5, \quad \alpha = e^5, \quad \mathfrak {g}/ {\mathfrak {z}}(\mathfrak {g}) = {\rm Span} \lbrace e_1, e_2, e_3, e_4 \rbraceand {\rm d} e^5 = 2 \Omega , where \Omega is the Kähler form on the quotient.4-dimensional Kähler Lie algebra... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 383,
"openalex_id": "",
"raw": "Ovando G.: Invariant pseudo-Kähler metrics in dimension four, J. Lie Theory 16 (2006), 371–391.",
"source_ref_id": "2fda1d77829a9effa2853c9a0ac5b0d61f52b1ba",
"start": 292
}
]
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
1401,
1543,
55076,
10,
18231,
99407,
28,
115187,
30591,
758,
111,
125458,
6000,
92,
177,
6044,
5134,
2203,
91526,
289,
14612,
8353,
169,
63438,
304,
363,
617,
104,
116,
87849,
83,
23734,
127,
603,
3173,
98,
41502,
18750,
35748,
157955,
... | [
0.06170654296875,
0.125244140625,
0.15966796875,
0.0321044921875,
0.264404296875,
0.1402587890625,
0.093017578125,
0.10015869140625,
0.1134033203125,
0.1571044921875,
0.0172119140625,
0.0204315185546875,
0.15185546875,
0.09832763671875,
0.1163330078125,
0.037109375,
0.2056884765625,
... | |
b42833dcab3b1e4f27d353e8298b08d66c9c7304 | subsection | 17 | 30 | Body | By using this classification we obtain that \mathfrak {g} is isomorphic to one of the following Lie algebras\begin{aligned}&{\mathfrak {k}}_1=\left(0,0,0,0,\lambda \,e^{12}+\mu \,e^{34}\right),\quad \lambda \,,\mu <0\,;\\
&{\mathfrak {k}}_2=\left(0,-e^{12},0,0,\lambda \,e^{12}+\mu \,e^{34}\right),\quad \lambda \,,\mu <... | {
"cite_spans": []
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
17368,
903,
40865,
113054,
41872,
125458,
6000,
92,
10666,
177,
8152,
83,
13882,
178851,
1771,
47,
1632,
70,
25632,
29730,
144,
429,
56095,
372,
6820,
143420,
297,
1230,
24854,
47391,
115187,
1369,
133,
2480,
132,
63527,
4,
143,
6492,
85,... | [
0.05804443359375,
0.0335693359375,
0.2047119140625,
0.061981201171875,
0.04388427734375,
0.1168212890625,
0.25048828125,
0.178466796875,
0.0174560546875,
0.22998046875,
0.02069091796875,
0.119140625,
0.16943359375,
0.2724609375,
0.1656494140625,
0.1669921875,
0.09210205078125,
0.01... | |
7d598bada7cf133f3b51c1f41349d67c5aee15bc | subsection | 18 | 30 | Body | Moreover, \mathfrak {g}_i (respectively \mathfrak {g}_i^{\delta }) is not isomorphic to \mathfrak {g}_k (respectively \mathfrak {g}_k^{\delta }) for any i \ne k.Applying again Proposition REF , it follows that the Lie algebras in the family {\mathfrak {g}}_7^{\delta } are not isomorphic one each other for different val... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 2052,
"openalex_id": "",
"raw": "Hasegawa, K.: A class of compact Kählerian solvmanifolds and a general conjecture, Geom. Dedicata 78 (1999), 253–258.",
"source_ref_id": "efc688d4bd1d184a4339f536ee2a88f8dac89879",
"sta... | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
5465,
125458,
6000,
92,
177,
14,
1743,
102,
83,
959,
13882,
178851,
1771,
47,
2499,
17,
472,
13438,
1250,
40322,
9069,
919,
29730,
144,
429,
56095,
14449,
966,
1632,
12638,
3789,
12921,
142424,
1019,
25632,
12116,
63708,
19844,
83279,
147... | [
0.013763427734375,
0.010894775390625,
0.166015625,
0.10986328125,
0.052642822265625,
0.06121826171875,
0.1114501953125,
0.11181640625,
0.01641845703125,
0.1177978515625,
0.093017578125,
0.2088623046875,
0.073974609375,
0.024932861328125,
0.042449951171875,
0.06231689453125,
0.0886230... | |
5d651e5bee34844aa75c60640de872a4ad1ce8e5 | subsection | 19 | 30 | Body | We recall that a solvmanifold is called completely solvable if the adjoint representation of the corresponding solvable Lie group has only real eigenvalues.Let ({\mathfrak {g}},\Phi ,\alpha ,\xi ,g) be a 5-dimensional Sasakian Lie algebra with trivial center and \mathfrak {g}^{\prime } = \mathfrak {g}. By the only cont... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 535,
"openalex_id": "",
"raw": "Diatta A.: Left-invariant contact structures on Lie groups, Diff. Geom. Appl. 26 (2008), no. 5, 544–552.",
"source_ref_id": "efec818fce4c7821e348bec597be35f5e2ab7f2b",
"start": 304
}... | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
189232,
132944,
9051,
42822,
35839,
64557,
2886,
2174,
606,
513,
4288,
18811,
29730,
21115,
1556,
4734,
2773,
8518,
27494,
90,
124480,
6000,
92,
177,
45689,
14,
14612,
5134,
8967,
157955,
94120,
301,
66,
144,
429,
2844,
1927,
686,
27585,
... | [
0.10284423828125,
0.2373046875,
0.1260986328125,
0.205078125,
0.0985107421875,
0.1505126953125,
0.21142578125,
0.008514404296875,
0.043701171875,
0.1202392578125,
0.08074951171875,
0.15087890625,
0.21728515625,
0.1588134765625,
0.00494384765625,
0.09283447265625,
0.1590576171875,
0... | |
b76efe5869168f66267e1eda20dee2e406e7134e | subsection | 20 | 30 | Body | \end{array}A 1-form \alpha =\sum _{i = 1}^5 a_i e^i is contact if and only if the real numbers a_i satisfy the condition\Delta := a_3 a_4^2 - a_2 a_5^2 - a_1 a_4 a_5 \ne 0.In this case, the corresponding Reeb vector is given by\xi = - \frac{1}{3 \Delta } \left( a_4 a_5 e_1 + a_5^2 e_2 - a_4^2 e_3 + (a_1 a_5 - 2 a_3 a_4... | {
"cite_spans": []
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
284,
4317,
5037,
289,
14612,
11832,
14,
758,
10,
28,
8353,
83,
5470,
2174,
4734,
2773,
101935,
40407,
35431,
58598,
102,
363,
617,
757,
42518,
853,
6403,
173,
18770,
34475,
5134,
132076,
43317,
12765,
1193,
6000,
24861,
70141,
1052,
304,
... | [
0.0794677734375,
0.079345703125,
0.24462890625,
0.070556640625,
0.2156982421875,
0.19384765625,
0.0731201171875,
0.18115234375,
0.0399169921875,
0.09375,
0.000732421875,
0.113037109375,
0.29443359375,
0.042327880859375,
0.045562744140625,
0.1361083984375,
0.155029296875,
0.10339355... | |
300b1b8e61a9af7def47d76b643d844f8867c529 | subsection | 21 | 30 | Body | Furthermore, taking into account that \alpha ([e_3,e_4])=-{\rm d}\alpha (e_3,e_4)=-2, and recalling that \theta :{\mathfrak {g}}\times {\mathfrak {g}}\rightarrow \ker \alpha denotes the projection of the bracket on {\mathfrak {g}} onto \ker \alpha , we have\begin{aligned}0=&[\xi ,[e_3,e_4]]+[e_4,[\xi ,e_3]]-[e_3,[\xi ,... | {
"cite_spans": []
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
9319,
17678,
15426,
41872,
289,
14612,
13,
363,
617,
268,
16,
9,
39,
104,
29557,
5428,
189232,
6,
2347,
102,
125458,
6000,
92,
177,
70141,
10666,
47391,
54969,
118201,
1728,
8,
157,
13452,
1830,
1620,
27853,
98,
188,
642,
765,
372,
68... | [
0.00128173828125,
0.034027099609375,
0.0718994140625,
0.015777587890625,
0.06866455078125,
0.215576171875,
0.09759521484375,
0.15869140625,
0.159912109375,
0.0158233642578125,
0.016357421875,
0.0226287841796875,
0.0950927734375,
0.1610107421875,
0.1641845703125,
0.169677734375,
0.106... | |
cb896b8b4ef2ec09325a115cb5e2a897f82cc169 | subsection | 22 | 30 | Body | From the vanishing of the coefficients of e^{ij5}, i, j = 1, \ldots , 4, in {\rm d}^2 e^k =0, k = 1, \ldots , 5, we get the following linear equationsc_2 - f_3 = f_2 + c_3 =0.Moreover,{\rm d}^2 e^5 = (a_6 + 2 c_4 + f_2 + c_3) e^{234} + (- b_6 + c_2 + f_3) e^{134}.and therefore in addition to (REF ) we havea_6 = -2 c_4,... | {
"cite_spans": []
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
28090,
131,
14,
54700,
552,
4240,
11044,
35066,
28,
13786,
758,
17,
1647,
106,
30591,
201,
23,
42,
39,
104,
8353,
304,
92,
145407,
472,
4,
190,
642,
2046,
25632,
192617,
13722,
5256,
238,
454,
1238,
363,
2203,
997,
501,
5,
910,
116,... | [
0.07666015625,
0.0941162109375,
0.0894775390625,
0.09710693359375,
0.1070556640625,
0.1138916015625,
0.1297607421875,
0.05010986328125,
0.110107421875,
0.1280517578125,
0.150634765625,
0.038360595703125,
0.1177978515625,
0.00531005859375,
0.07159423828125,
0.0992431640625,
0.03128051... | |
93b5245b65347d4fd3ebab9cc663e44527470847 | subsection | 23 | 30 | Body | \end{aligned}In the first two cases, we have that{\rm A}1), \, {\rm A} 2)\simeq \mathfrak {aff}({\mathbb {R}})\times \mathfrak {sl}(2,{\mathbb {R}})where respectively{\rm A}1) {\left\lbrace \begin{array}{ll}
\begin{aligned}&\mathfrak {aff}({\mathbb {R}})\simeq {\rm Span}\lbrace f_4\,e_1-c_3\,e_2,e_1-c_3\,e_5\rbrace \,,... | {
"cite_spans": []
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
41872,
143420,
297,
4153,
5117,
6626,
50218,
642,
765,
450,
39,
62,
17727,
4,
8152,
4958,
13777,
864,
125458,
6000,
92,
62566,
132,
5125,
1052,
47391,
70141,
24861,
54753,
136913,
107013,
2480,
99407,
6820,
19305,
1181,
1230,
10666,
63438,
... | [
0.01287841796875,
0.1534423828125,
0.010986328125,
0.0687255859375,
0.09979248046875,
0.1422119140625,
0.2156982421875,
0.07525634765625,
0.13916015625,
0.1688232421875,
0.051544189453125,
0.1485595703125,
0.095947265625,
0.08978271484375,
0.002532958984375,
0.16015625,
0.20629882812... | |
5f1974eec787535768f334928e84e1a72579d5b0 | subsection | 24 | 30 | Body | \end{aligned}
\end{array}\right.}In the other cases we see that{\rm A}3), {\rm A}4) \cong {\mathbb {R}}^2 \ltimes {\mathfrak {h}}_3by using for A3) the new basis\left\lbrace E_1 = a_1 e_1 + 2 e_5, E_2 = \frac{1}{a_1} e_2, E_j = e_j, j =3,4,5\right\rbrace ,with {\mathbb {R}}^2 = {\rm {Span}} \lbrace E_2, E_5 \rbrace , \... | {
"cite_spans": []
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
3611,
143420,
297,
6,
19305,
53,
54969,
4153,
70,
3789,
50218,
642,
1957,
39,
62,
21320,
41872,
29557,
587,
449,
10666,
125458,
5125,
1052,
8353,
304,
141,
70141,
6000,
92,
127,
363,
1272,
17368,
100,
3525,
18231,
2480,
99407,
241,
1151... | [
0.0208740234375,
0.18701171875,
0.065185546875,
0.0164031982421875,
0.09375,
0.054229736328125,
0.06060791015625,
0.0186004638671875,
0.0311737060546875,
0.12939453125,
0.1798095703125,
0.01336669921875,
0.1143798828125,
0.01336669921875,
0.150146484375,
0.2166748046875,
0.0064392089... | |
c90b0597e2246e9a29a95c763256a938aad117e5 | subsection | 25 | 30 | Body | \end{aligned}Condition N_{\Phi }=-{\rm d} e^5 \otimes e_5 implies the following linear equationsc_5=c_2-f_3-f_4\,,\,f_5=f_2+c_3+c_4\,,while {\rm d}^2=0 givesc_2=f_3\,,\,
f_2=-c_3\,,\,a_6=-2c_4\,,\,f_3=\frac{1}{2}b_6\,.Hence the structure equations (REF ) of {\mathfrak {g}} reduces to\begin{aligned}&{\rm d}e^1=a_1\,e^{1... | {
"cite_spans": []
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
6,
3611,
143420,
11935,
428,
1363,
541,
454,
45689,
14,
1369,
9,
24854,
39,
104,
28,
8353,
758,
31,
70141,
35388,
90,
25632,
192617,
13722,
5256,
238,
18504,
420,
27495,
617,
41872,
4,
304,
1328,
363,
204610,
42,
8152,
145407,
76199,
... | [
0.042755126953125,
0.013153076171875,
0.1165771484375,
0.08935546875,
0.183837890625,
0.0628662109375,
0.1502685546875,
0.04339599609375,
0.1617431640625,
0.18212890625,
0.0289764404296875,
0.1002197265625,
0.0133056640625,
0.048004150390625,
0.160400390625,
0.1285400390625,
0.058380... | |
c1cb6ab20d123ec2663e4465124f41775379df8c | subsection | 26 | 30 | Body | \end{aligned}In the first two cases we have{\rm B}1)\,,\,{\rm B}2)\simeq \mathfrak {aff}({\mathbb {R}})\times \mathfrak {su}(2)\,,where respectively{\rm B}1) {\left\lbrace \begin{array}{ll}
\begin{aligned}&\mathfrak {aff}({\mathbb {R}})\simeq {\rm Span}\lbrace a_1\,e_1+ e_5\,,f_4\,e_1+e_5\rbrace \\
&\mathfrak {su}(2)\s... | {
"cite_spans": []
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
6,
41872,
143420,
297,
8152,
4153,
5117,
6626,
50218,
642,
765,
39,
335,
17727,
4,
24854,
10461,
13777,
864,
125458,
6000,
92,
62566,
5125,
1052,
47391,
70141,
1159,
40970,
136913,
107013,
2480,
99407,
6820,
19305,
1181,
1230,
63438,
10,
... | [
0.0176239013671875,
0.0389404296875,
0.1478271484375,
0.0290069580078125,
0.0028076171875,
0.07763671875,
0.1038818359375,
0.142333984375,
0.212890625,
0.081787109375,
0.1260986328125,
0.06732177734375,
0.140869140625,
0.09857177734375,
0.04168701171875,
0.024658203125,
0.14562988281... | |
c9be59ef80f79085bb049d708b8e9f1f06f5d432 | subsection | 27 | 30 | Body | \end{aligned}
\end{array}\right.}Again in the cases
{\rm B}3) and {\rm B}4) {\mathfrak {g}} is solvable and{\rm B}3), {\rm B}4) \cong {\mathbb {R}}^2 \ltimes {\mathfrak {h}}_3\,by using for B3) the new basis\left\lbrace G_1 = a_1 e_1 + 2 e_5, G_2 = \frac{1}{a_1} e_2, G_j = e_j, j =3,4,5\right\rbrace ,with {\mathbb {R}}... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 2296,
"openalex_id": "",
"raw": "Diatta A.: Left-invariant contact structures on Lie groups, Diff. Geom. Appl. 26 (2008), no. 5, 544–552.",
"source_ref_id": "efec818fce4c7821e348bec597be35f5e2ab7f2b",
"start": 2121
... | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
143420,
297,
8152,
6,
19305,
53,
41872,
54969,
284,
208,
23,
70,
50218,
42,
39,
335,
21320,
136,
10666,
29557,
125458,
6000,
92,
177,
47391,
83,
132944,
2886,
24854,
4,
587,
449,
5125,
1052,
8353,
304,
141,
70141,
127,
454,
363,
1272,... | [
0.068359375,
0.030792236328125,
0.031524658203125,
0.03125,
0.0233917236328125,
0.004150390625,
0.03143310546875,
0.0290069580078125,
0.0308837890625,
0.0499267578125,
0.02996826171875,
0.031585693359375,
0.139404296875,
0.03155517578125,
0.053375244140625,
0.125732421875,
0.17749023... | |
b7ac70dbe2303feb8746373b35541c82159468bc | subsection | 28 | 30 | Body | A Sasakian Lie algebra ({\mathfrak {g}},\Phi ,\alpha ,\xi ,g) is called \alpha -Einstein if the Ricci tensor {\rm Ric}_g of the metric g satisfies {\rm Ric}_g = \lambda g + \nu \,\alpha \otimes \alpha for some \lambda , \,\nu \in {\mathbb {R}}.It is known that the canonical Sasakian structure on \mathfrak {h}_5 is \alp... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 523,
"openalex_id": "",
"raw": "de Andrés L. C., Fernández M., Fino A., Ugarte L., Contact 5-manifolds with SU(2)-structure, preprint arXiv:0706.0386, to appear in Q. J. Math.",
"source_ref_id": "5a5c91111ed1a6ca9335913bfcca... | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
62,
94120,
301,
66,
29730,
144,
429,
2844,
6000,
92,
177,
47391,
4,
45689,
14,
6,
289,
14612,
5134,
16,
83,
35839,
41872,
20,
61061,
18055,
2174,
212071,
1492,
4970,
2975,
238,
8152,
186518,
706,
40407,
3387,
10666,
42,
39,
454,
2203,... | [
0.062103271484375,
0.19287109375,
0.2320556640625,
0.151611328125,
0.222900390625,
0.09381103515625,
0.158935546875,
0.175537109375,
0.203857421875,
0.09765625,
0.1207275390625,
0.012115478515625,
0.011962890625,
0.06378173828125,
0.0494384765625,
0.01190185546875,
0.0828857421875,
... | |
764a244983fc74db7389f592e29e35f9ab5bdfcd | subsection | 29 | 30 | Body | In the case B1) the Ricci tensor is given by{\rm Ric}_g=\begin{pmatrix}
-(2+a_1^2) &0 &0 &0 &0\\
0 &-(2+a_1^2) &0 &0 &0\\
0 &0 &0 &0 &0\\
0 &0 &0 &0 &0\\
0 &0 &0 &0 &4\\
\end{pmatrix}\,,whereas in the case B2) it is given by{\rm Ric}_g=\begin{pmatrix}
-(2+a_1^2+b_1^2) &0 &0 &0 &0\\
0 &-(2+a_1^2+b_1^2) &0 &0 &0\\
0 &0 &... | {
"cite_spans": []
} | 0807.1800 | A class of Sasakian 5-manifolds | [
"Adrian Andrada",
"Anna Fino",
"Luigi Vezzoni"
] | [
"math.DG"
] | 2,008 | en | Mathematics | [
7225,
335,
17727,
70,
212071,
1492,
4970,
34475,
390,
2975,
238,
177,
6820,
87427,
20,
54753,
1328,
11,
115187,
10461,
757,
9,
617,
442,
94120,
301,
66,
45646,
903,
29730,
144,
429,
2844,
8306,
40407,
14612,
61061,
18055,
35431,
10554,
... | [
0.1455078125,
0.1016845703125,
0.122314453125,
0.011566162109375,
0.28564453125,
0.2025146484375,
0.2413330078125,
0.1163330078125,
0.0128173828125,
0.0931396484375,
0.084716796875,
0.0914306640625,
0.0169219970703125,
0.0771484375,
0.0086669921875,
0.01519775390625,
0.10394287109375... | |
2770fb7319b430690bb6afc00e64a73d4c8e7fd4 | abstract | 0 | 8 | Abstract | We propose a scheme to realize the fractional quantum Hall system with atoms
confined in a two-dimensional array of coupled cavities. Our scheme is based on
simple optical manipulation of atomic internal states and inter-cavity hopping
of virtually excited photons. It is shown that as well as the fractional
quantum Hal... | {
"cite_spans": []
} | 10.1103/PhysRevLett.101.246809 | 0807.1802 | Fractional Quantum Hall State in Coupled Cavities | [
"Jaeyoon Cho",
"Dimitris G. Angelakis",
"Sougato Bose"
] | [
"quant-ph",
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
1401,
26171,
150370,
92154,
175921,
289,
110436,
19449,
5426,
678,
34627,
17438,
14534,
23,
6626,
9,
157955,
10298,
53,
111,
24941,
71,
151517,
2449,
22929,
35509,
8781,
233,
70760,
45258,
1363,
70796,
117249,
1940,
408,
3760,
739,
26783,
2... | [
0.0084228515625,
0.180419921875,
0.2056884765625,
0.2142333984375,
0.217041015625,
0.1107177734375,
0.177001953125,
0.25244140625,
0.1956787109375,
0.050933837890625,
0.2264404296875,
0.18359375,
0.0843505859375,
0.01251220703125,
0.103271484375,
0.00872802734375,
0.12548828125,
0.... |
e561d5e8c380cf9e9de0b268683933b788f6b1ea | subsection | 1 | 8 | Body | Fractional Quantum Hall State in Coupled CavitiesJaeyoon ChoDepartment of Physics and Astronomy, University College London, Gower St., London WC1E 6BT, UKCentre for Quantum Technologies, National University of Singapore,
2 Science Drive 3, Singapore 117542Dimitris G. AngelakisCentre for Quantum Technologies, National U... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1663,
"openalex_id": "",
"raw": "M. Lewenstein et al., Adv. Phys. 56, 243 (2007).",
"source_ref_id": "b3e3b6b0702b872bc42da50fdfa11f2e0652e8d9",
"start": 1433
},
{
"arxiv_id": "",
"doi": "",
"... | 10.1103/PhysRevLett.101.246809 | 0807.1802 | Fractional Quantum Hall State in Coupled Cavities | [
"Jaeyoon Cho",
"Dimitris G. Angelakis",
"Sougato Bose"
] | [
"quant-ph",
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
7868,
10763,
289,
75344,
316,
19449,
22836,
23,
1311,
2037,
6259,
2041,
686,
2449,
6979,
7460,
16762,
4960,
17365,
674,
111,
165712,
7,
136,
85303,
53,
12535,
29693,
9020,
2016,
6488,
2907,
5,
37808,
647,
305,
52681,
4,
17274,
59441,
13... | [
0.216064453125,
0.1405029296875,
0.06280517578125,
0.1785888671875,
0.1107177734375,
0.291748046875,
0.1875,
0.04669189453125,
0.085693359375,
0.17822265625,
0.1099853515625,
0.1409912109375,
0.2088623046875,
0.04962158203125,
0.0251007080078125,
0.046295166015625,
0.163818359375,
... |
b1308de45b88d36a9da8717862d11dce39db50ef | subsection | 2 | 8 | Body | Recently, theoretical works have shown that the Mott-superfluid phase transition of polaritons , and the Heisenberg spin chains can be realized in CCAs.
These works, however, relied only on globally addressing lasers and thus could not highlight the key advantage of CCAs, namely, the individual addressability in the s... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 154,
"openalex_id": "",
"raw": "M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, Nature Phys. 2, 849 (2006); D. G. Angelakis, M. F. Santos, and S. Bose, Phys. Rev. A 76, 031805(R) (2007); A. D. Greentree et al, Nature Phys. ... | 10.1103/PhysRevLett.101.246809 | 0807.1802 | Fractional Quantum Hall State in Coupled Cavities | [
"Jaeyoon Cho",
"Dimitris G. Angelakis",
"Sougato Bose"
] | [
"quant-ph",
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
169549,
538,
4,
4524,
43240,
127887,
33637,
18,
59104,
18026,
532,
93402,
149307,
160,
1703,
67772,
6,
19614,
48467,
25927,
121293,
831,
186,
185171,
23,
21581,
19659,
28702,
297,
98,
7964,
29823,
214,
32030,
7,
136,
959,
127308,
70,
2279... | [
0.03094482421875,
0.0238494873046875,
0.0239410400390625,
0.0261077880859375,
0.0899658203125,
0.039337158203125,
0.1123046875,
0.0711669921875,
0.086669921875,
0.142578125,
0.000396728515625,
0.156494140625,
0.1597900390625,
0.068603515625,
0.081298828125,
0.1131591796875,
0.0239715... |
e2dec01a102d45b22b8463dc3b88b1a8e0f54754 | subsection | 3 | 8 | Body | Although in this work we mainly consider the
FQH systems, another great advantage is that unlike the previous schemes for optical lattices
any Abelian vector potential on a lattice can be also simulated simply by
adjusting the laser phases in accordance with the
formula (REF ). The creation of a quasiexcitation, which ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 526,
"openalex_id": "",
"raw": "R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).",
"source_ref_id": "edff678a5368a59883589b7f85c9d3e97721583f",
"start": 279
},
{
"arxiv_id": "",
"doi": "",
"e... | 10.1103/PhysRevLett.101.246809 | 0807.1802 | Fractional Quantum Hall State in Coupled Cavities | [
"Jaeyoon Cho",
"Dimitris G. Angelakis",
"Sougato Bose"
] | [
"quant-ph",
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
106073,
23,
4488,
5201,
538,
16916,
563,
2737,
841,
76519,
4,
15700,
6782,
92940,
5062,
70,
96362,
150370,
7,
100,
233,
70760,
21,
3771,
5170,
2499,
113140,
3378,
173,
18770,
38516,
98,
10495,
24494,
831,
186,
2843,
40226,
3674,
42856,
... | [
0.0428466796875,
0.0284881591796875,
0.042205810546875,
0.046875,
0.028594970703125,
0.07598876953125,
0.120361328125,
0.1552734375,
0.197265625,
0.2027587890625,
0.02862548828125,
0.065185546875,
0.09515380859375,
0.1988525390625,
0.07525634765625,
0.028564453125,
0.0333251953125,
... |
f931b7139f9f7ddf19cd50942a706f69bb284f53 | subsection | 4 | 8 | Body | In the rotating frame, the
Hamiltonian readswhere J^{X} (J^{Y}) denotes the inter-cavity hopping rate of
the photon along the \hat{x} (\hat{y}) direction, and the subscript
(p,q) represents the cavity site. As mentioned above, we assume
\Delta ^{X}-\Delta ^{Y}\gg g^{X},g^{Y}, and also assume \Delta ^{\mu }\gg g^{\mu }\... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1175,
"openalex_id": "",
"raw": "D. F. V. James and J. Jerke, Can. J. Phys. 85, 625 (2007).",
"source_ref_id": "6055270877707770c8f58ade35599c8208f372f4",
"start": 1060
}
]
} | 10.1103/PhysRevLett.101.246809 | 0807.1802 | Fractional Quantum Hall State in Coupled Cavities | [
"Jaeyoon Cho",
"Dimitris G. Angelakis",
"Sougato Bose"
] | [
"quant-ph",
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
360,
47014,
1916,
123789,
70,
94674,
3378,
12301,
136913,
821,
1542,
8152,
1375,
1723,
16,
8,
157,
1636,
1940,
408,
3760,
53,
739,
26783,
34515,
16186,
19,
33233,
6,
2943,
24854,
425,
15,
48225,
4,
1614,
32032,
254,
864,
33636,
7,
151... | [
0.0284881591796875,
0.178466796875,
0.1107177734375,
0.222900390625,
0.0220184326171875,
0.273193359375,
0.240478515625,
0.1695556640625,
0.038665771484375,
0.1065673828125,
0.08349609375,
0.022125244140625,
0.0836181640625,
0.09429931640625,
0.0218658447265625,
0.07891845703125,
0.1... |
dbb1ab618c72a9696b87f1c7f04706cde8b95d11 | subsection | 5 | 8 | Body | In view of the fact that the cavity photon is suppressed, we restrict
our calculation to the subspace wherein the maximum number of excitations
in a cavity is limited to one, i.e., \langle a_{p,q}^{X\dagger }a_{p,q}^{X}+a_{p,q}^{Y\dagger }a_{p,q}^{Y}+\left(\left|1\right>\left<1\right|\right)_{p,q}\rangle \le 1.
Up to t... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 457,
"openalex_id": "",
"raw": "F. D. M. Haldane, Phys. Rev. Lett. 55, 2095 (1985); F. D. M. Haldane and E. H. Rezayi, Phys. Rev. B 31, 2529 (1985).",
"source_ref_id": "150e6ca79f6d934f57e084e192ef5305dd3bccd3",
"start... | 10.1103/PhysRevLett.101.246809 | 0807.1802 | Fractional Quantum Hall State in Coupled Cavities | [
"Jaeyoon Cho",
"Dimitris G. Angelakis",
"Sougato Bose"
] | [
"quant-ph",
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
21455,
111,
70,
151517,
939,
16186,
19,
83,
15811,
11856,
297,
173072,
74481,
1614,
65421,
38132,
14012,
164101,
5256,
23,
84046,
47,
1632,
4,
17,
5,
13,
6,
3066,
133,
10,
24854,
864,
8152,
1542,
85,
21407,
51912,
11,
454,
254,
8353,
... | [
0.05108642578125,
0.01080322265625,
0.01104736328125,
0.2401123046875,
0.1827392578125,
0.177734375,
0.0770263671875,
0.038909912109375,
0.121826171875,
0.191162109375,
0.01055908203125,
0.1475830078125,
0.1766357421875,
0.1849365234375,
0.2012939453125,
0.1458740234375,
0.0778198242... |
f1f34c8b1111d5412f18ef8a18132e078df1e5a0 | subsection | 6 | 8 | Body | From this figure, it is apparent that the Laughlin
ground state can be prepared by the following procedure: (1) Prepare
the atoms in state \left|1\right> at sites chosen evenly in agreement
with the filling factor \nu , with all other atoms prepared in state
\left|0\right>. Initially all lasers are turned off; (2) Appl... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 870,
"openalex_id": "",
"raw": "R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).",
"source_ref_id": "edff678a5368a59883589b7f85c9d3e97721583f",
"start": 699
},
{
"arxiv_id": "",
"doi": "",
"e... | 10.1103/PhysRevLett.101.246809 | 0807.1802 | Fractional Quantum Hall State in Coupled Cavities | [
"Jaeyoon Cho",
"Dimitris G. Angelakis",
"Sougato Bose"
] | [
"quant-ph",
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
28090,
26366,
4,
173676,
239,
58968,
2397,
61585,
11341,
831,
186,
133888,
390,
70,
25632,
50491,
798,
1914,
16082,
34627,
7,
23,
6,
41872,
133,
2480,
54969,
2740,
99,
15271,
19667,
19,
538,
106689,
678,
26292,
214,
31461,
58745,
2389,
... | [
0.0050048828125,
0.1676025390625,
0.00689697265625,
0.09698486328125,
0.130126953125,
0.2425537109375,
0.2822265625,
0.21923828125,
0.201416015625,
0.0863037109375,
0.03704833984375,
0.224365234375,
0.0191802978515625,
0.013641357421875,
0.041290283203125,
0.1551513671875,
0.02395629... |
86057713686b70863ef555a547cbe621fc3b6ab0 | subsection | 7 | 8 | Body | If we choose those frequencies so that \left|\omega _{1}-\omega _{2}\right|\sim \delta ^{\mu },
they do not produce the spin exchange to the \hat{y} direction.
In the same manner, we apply lasers with frequencies \omega _{3}
and \omega _{4} in every second column to produce the spin exchange
to the \hat{y} direction. B... | {
"cite_spans": []
} | 10.1103/PhysRevLett.101.246809 | 0807.1802 | Fractional Quantum Hall State in Coupled Cavities | [
"Jaeyoon Cho",
"Dimitris G. Angelakis",
"Sougato Bose"
] | [
"quant-ph",
"cond-mat.mes-hall"
] | 2,008 | en | Physics | [
4263,
642,
55076,
8382,
12478,
944,
117538,
2480,
306,
2765,
418,
304,
54969,
5072,
1743,
102,
561,
54,
959,
27489,
25927,
121122,
47,
2943,
53,
48225,
59911,
32030,
7,
678,
363,
617,
11907,
17932,
3365,
316,
70,
218873,
22759,
129980,
... | [
0.049774169921875,
0.0142364501953125,
0.1676025390625,
0.0865478515625,
0.1964111328125,
0.14599609375,
0.10760498046875,
0.044525146484375,
0.1083984375,
0.1949462890625,
0.0171356201171875,
0.03692626953125,
0.06085205078125,
0.169677734375,
0.08013916015625,
0.0960693359375,
0.13... |
ffdc1f834e3881f9a65a32cbda771f5509bdd881 | abstract | 0 | 16 | Abstract | We propose a principle of consistency between different hierarchical levels
of biological systems. Given a consistency between molecule replication and
cell reproduction, universal statistical laws on cellular chemical abundances
are derived and confirmed experimentally. They include a power law distribution
of gene ex... | {
"cite_spans": []
} | 0807.1803 | Consistency Principle in Biological Dynamical Systems | [
"Kunihiko Kaneko",
"Chikara Furusawa"
] | [
"q-bio.CB",
"cond-mat.stat-mech",
"nlin.AO",
"q-bio.PE",
"q-bio.SC"
] | 2,008 | en | Quantitative Biology | [
1401,
26171,
24702,
133,
35060,
27771,
17721,
12921,
1791,
54689,
90926,
333,
109622,
76519,
49711,
75449,
456,
182867,
136,
38750,
42238,
32813,
80835,
131703,
2927,
120087,
165045,
130807,
3956,
16406,
39563,
195935,
14537,
27165,
113068,
22293... | [
0.023590087890625,
0.152587890625,
0.177001953125,
0.064697265625,
0.271728515625,
0.182373046875,
0.1339111328125,
0.1256103515625,
0.1075439453125,
0.1451416015625,
0.17333984375,
0.07659912109375,
0.0243988037109375,
0.1533203125,
0.0970458984375,
0.09051513671875,
0.0943603515625... | |
1a5c3d495be14827cd8bd9085ad7508b86ab3635 | subsection | 1 | 16 | Introduction | Biological systems generally form a hierarchy. Ecological systems consist of a population of organisms, an organism consists of an ensemble of cells, and a cell consists of interacting biomolecules. Of course, such hierarchical structures also exist in nonliving systems. Then, is there some characteristic property unde... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1782,
"openalex_id": "",
"raw": "K. Kaneko and I Tsuda, Complex Systems: Chaos and Beyond, Springer 2000.",
"source_ref_id": "2898022c5189e9f5bf8ed8abb230f98b2b67c6d3",
"start": 1524
},
{
"arxiv_id": "",
... | 0807.1803 | Consistency Principle in Biological Dynamical Systems | [
"Kunihiko Kaneko",
"Chikara Furusawa"
] | [
"q-bio.CB",
"cond-mat.stat-mech",
"nlin.AO",
"q-bio.PE",
"q-bio.SC"
] | 2,008 | en | Quantitative Biology | [
1843,
109622,
76519,
137567,
3173,
10,
1791,
147,
7668,
5,
74242,
58055,
111,
43904,
25150,
7,
4,
142,
63304,
38750,
136,
78974,
214,
3530,
432,
133,
70838,
6619,
6044,
54689,
6827,
45646,
2843,
32316,
23,
351,
150,
6496,
47009,
83,
268... | [
0.220947265625,
0.2247314453125,
0.283203125,
0.15869140625,
0.189208984375,
0.1029052734375,
0.2061767578125,
0.199462890625,
0.169677734375,
0.028900146484375,
0.18701171875,
0.158203125,
0.025787353515625,
0.150634765625,
0.1993408203125,
0.02587890625,
0.0258026123046875,
0.025... | |
4ed91b8e0730b8ec9d6f43ee20cf0ce43bd661e7 | subsection | 2 | 16 | Introduction | In question is how such consistency between different levels is sustained and whether there are resulting universal laws that apply to all biological systems.Here we attempt to answer these questions by considering three examples: statistical laws
representing consistency between molecule replication and cell reproduct... | {
"cite_spans": []
} | 0807.1803 | Consistency Principle in Biological Dynamical Systems | [
"Kunihiko Kaneko",
"Chikara Furusawa"
] | [
"q-bio.CB",
"cond-mat.stat-mech",
"nlin.AO",
"q-bio.PE",
"q-bio.SC"
] | 2,008 | en | Quantitative Biology | [
9655,
3642,
6044,
35060,
27771,
17721,
12921,
90926,
83,
205027,
297,
16750,
32813,
131703,
59911,
756,
333,
109622,
76519,
642,
81887,
35166,
17582,
179635,
17262,
27781,
80835,
289,
33636,
49711,
75449,
456,
182867,
136,
38750,
42238,
4537,
... | [
0.125,
0.06103515625,
0.07720947265625,
0.2408447265625,
0.15771484375,
0.1077880859375,
0.1241455078125,
0.1937255859375,
0.011016845703125,
0.1866455078125,
0.06549072265625,
0.05218505859375,
0.148193359375,
0.2054443359375,
0.0902099609375,
0.032470703125,
0.0958251953125,
0.06... | |
69c1de61f343cfe5e44468452ffb416a2bff4776 | subsection | 3 | 16 | Reaction network for cell reproduction | A cell consists of several replicating molecular species that help in the synthesis of new molecules through catalytic reactions. As a result, a cell grows until it divides to produce two cells with similar chemical compositions (see Fig.2).
[Figure: Basic structure of a reproducing cell with internal catalytic chemica... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1159,
"openalex_id": "",
"raw": "Furusawa, C., and Kaneko, K., Phys. Rev. Lett. 2003, 90, 088102.",
"source_ref_id": "32437d6df27a5f4c8db6b2ba2445e94246685e8b",
"start": 912
},
{
"arxiv_id": "",
"do... | 0807.1803 | Consistency Principle in Biological Dynamical Systems | [
"Kunihiko Kaneko",
"Chikara Furusawa"
] | [
"q-bio.CB",
"cond-mat.stat-mech",
"nlin.AO",
"q-bio.PE",
"q-bio.SC"
] | 2,008 | en | Quantitative Biology | [
62,
38750,
58055,
7,
111,
40368,
143126,
1916,
233239,
114149,
4358,
23,
70,
142518,
90,
3525,
49711,
70838,
8305,
60199,
538,
9523,
132539,
1301,
10,
16750,
4,
55993,
24189,
101637,
27489,
6626,
678,
21373,
165045,
166577,
15,
21231,
11989... | [
0.1129150390625,
0.283203125,
0.1376953125,
0.046905517578125,
0.035125732421875,
0.109130859375,
0.292724609375,
0.1129150390625,
0.1064453125,
0.1741943359375,
0.148681640625,
0.030426025390625,
0.031097412109375,
0.0986328125,
0.0302886962890625,
0.0697021484375,
0.1058349609375,
... | |
278bd422ff1c08064965c4acec2852e7db14b93b | subsection | 4 | 16 | Universal power law in chemical abundances over species | We investigated the universal statistical characteristics of reproduction state. First, we studied the statistics on the abundance of chemicals for a cell undergoing reproduction with constant chemical compositions. We measured the rank-ordered distributions of chemical species by plotting the number of molecules n_i a... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 478,
"openalex_id": "",
"raw": "Furusawa, C., and Kaneko, K., Phys. Rev. Lett. 2003, 90, 088102.",
"source_ref_id": "32437d6df27a5f4c8db6b2ba2445e94246685e8b",
"start": 369
},
{
"arxiv_id": "",
"doi... | 0807.1803 | Consistency Principle in Biological Dynamical Systems | [
"Kunihiko Kaneko",
"Chikara Furusawa"
] | [
"q-bio.CB",
"cond-mat.stat-mech",
"nlin.AO",
"q-bio.PE",
"q-bio.SC"
] | 2,008 | en | Quantitative Biology | [
1401,
32603,
3674,
32813,
80835,
289,
62816,
48242,
111,
42238,
1363,
11341,
23972,
4,
642,
22282,
70,
7,
130807,
3956,
165045,
38750,
1379,
519,
678,
53697,
166577,
72350,
30648,
80596,
297,
113068,
114149,
390,
23577,
1916,
14012,
49711,
... | [
0.025115966796875,
0.1314697265625,
0.048095703125,
0.2132568359375,
0.247802734375,
0.063232421875,
0.1708984375,
0.1109619140625,
0.04815673828125,
0.275146484375,
0.1317138671875,
0.1641845703125,
0.03350830078125,
0.04815673828125,
0.006744384765625,
0.07275390625,
0.048126220703... | |
54f0ec81aba2ca1c0bfc4be0210d3fd254c603d1 | subsection | 5 | 16 | Universal lognormal distribution of chemical abundances in cells | We have thus far examined the average abundance of each chemical. Because the chemical reaction process is stochastic, the number of each type of molecule differs between cells. We therefore studied the distribution of each molecule number, sampled among cells, to find that the distribution is fitted reasonably well by... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 873,
"openalex_id": "",
"raw": "Furusawa C. et al. (2005) BIOPHYSICS 1, 25-31.",
"source_ref_id": "e73a4c0124f6d2043c26f05585fc8f1506f01604",
"start": 669
}
]
} | 0807.1803 | Consistency Principle in Biological Dynamical Systems | [
"Kunihiko Kaneko",
"Chikara Furusawa"
] | [
"q-bio.CB",
"cond-mat.stat-mech",
"nlin.AO",
"q-bio.PE",
"q-bio.SC"
] | 2,008 | en | Quantitative Biology | [
4911,
7,
2060,
160477,
83080,
130807,
3956,
12638,
165045,
88949,
132539,
9433,
83,
3474,
1436,
28692,
4,
70,
14012,
111,
10644,
49711,
75449,
129927,
17721,
38750,
22282,
113068,
121413,
71,
54940,
112031,
31635,
78458,
5299,
390,
12684,
331... | [
0.0128173828125,
0.0150146484375,
0.0843505859375,
0.0843505859375,
0.1917724609375,
0.252685546875,
0.1339111328125,
0.109619140625,
0.2369384765625,
0.0233001708984375,
0.2325439453125,
0.1461181640625,
0.023193359375,
0.10516357421875,
0.1395263671875,
0.10357666015625,
0.01443481... | |
bfefdca55cbaa9e6b63223233bf288b6b0271c76 | subsection | 6 | 16 | Universal lognormal distribution of chemical abundances in cells | A portion of possible reaction pathways are used dominantly, which organizes a cascade of catalytic reactions so that a chemical in the i-th group is catalyzed by the (i+1)-th, and that in the (i+1)-th group is catalyzed by the (i+2)-th, and so forth. A “modular structure” with groups of successive catalytic reactions ... | {
"cite_spans": []
} | 0807.1803 | Consistency Principle in Biological Dynamical Systems | [
"Kunihiko Kaneko",
"Chikara Furusawa"
] | [
"q-bio.CB",
"cond-mat.stat-mech",
"nlin.AO",
"q-bio.PE",
"q-bio.SC"
] | 2,008 | en | Quantitative Biology | [
126826,
7722,
132539,
60875,
102966,
11814,
73944,
4,
5808,
90,
130391,
112,
60199,
538,
9523,
7,
221,
165045,
17,
927,
21115,
64807,
14,
21748,
54651,
5,
83279,
147,
45646,
94407,
208479,
15970,
53404,
33120,
14838,
41039,
21094,
118126,
9... | [
0.09210205078125,
0.16455078125,
0.1973876953125,
0.1087646484375,
0.138671875,
0.15283203125,
0.1953125,
0.016845703125,
0.17822265625,
0.032562255859375,
0.1448974609375,
0.10223388671875,
0.170166015625,
0.1419677734375,
0.07232666015625,
0.04888916015625,
0.012542724609375,
0.2... | |
d12ed2471c6f939b605f32ec2f30954847b1e6b5 | subsection | 7 | 16 | Embedding the abundance power law into network topology | Next, we investigated the relationship between the network connectivity statistics and the abundance statistics. The distributions in the connectivity of reaction networks has been studied extensively , , while the power law in chemical abundances discussed here is independent of the network structure, as long as the c... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 365,
"openalex_id": "",
"raw": "Jeong, H., Tombor, B., Albert, R., Oltvai, Z. N., and Barabási, A.-L., Nature 2003, 407, 651.",
"source_ref_id": "24e4bb2656576a88a566621b50b6282f90fedb6c",
"start": 113
},
{
... | 0807.1803 | Consistency Principle in Biological Dynamical Systems | [
"Kunihiko Kaneko",
"Chikara Furusawa"
] | [
"q-bio.CB",
"cond-mat.stat-mech",
"nlin.AO",
"q-bio.PE",
"q-bio.SC"
] | 2,008 | en | Quantitative Biology | [
4997,
642,
32603,
70,
76755,
17721,
33120,
37067,
54613,
53,
80835,
7,
136,
130807,
3956,
113068,
23,
132539,
2809,
22282,
71,
1119,
41745,
272,
538,
6,
4,
12960,
14537,
27165,
165045,
297,
83,
41371,
111,
45646,
237,
4989,
38750,
40407,
... | [
0.016021728515625,
0.0133056640625,
0.111328125,
0.040679931640625,
0.1661376953125,
0.045928955078125,
0.2435302734375,
0.2353515625,
0.2022705078125,
0.055267333984375,
0.2362060546875,
0.0275421142578125,
0.06829833984375,
0.2744140625,
0.1591796875,
0.239013671875,
0.060363769531... | |
e2d7161a3143af0c41b54bb30a933b25368bdc60 | subsection | 8 | 16 | Evolutionary fluctuation response relationship | The result of §2.3 suggests the existence of large phenotypic fluctuations among cells with identical genes. In the model, the network and the parameters are identical, and in the experiment, isogenic bacteria are used. Still, there exist large isogenic phenotypic fluctuations. Here we discuss the relevance of such flu... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1385,
"openalex_id": "",
"raw": "Sato K., Ito Y., Yomo T., and Kaneko K. (2003) (2003) Proc. Nat. Acad. Sci. USA 100, 14086-14090.",
"source_ref_id": "555991ab0bf995097f30992d8ce7ab81f1b7ff54",
"start": 1184
},
... | 0807.1803 | Consistency Principle in Biological Dynamical Systems | [
"Kunihiko Kaneko",
"Chikara Furusawa"
] | [
"q-bio.CB",
"cond-mat.stat-mech",
"nlin.AO",
"q-bio.PE",
"q-bio.SC"
] | 2,008 | en | Quantitative Biology | [
16750,
5360,
120883,
42459,
6,
116311,
21334,
88322,
72057,
18695,
14838,
41039,
21094,
54940,
38750,
7,
678,
31943,
6827,
22293,
360,
70,
3299,
4,
33120,
171859,
621,
136,
23,
28007,
83,
62976,
1771,
152818,
11814,
50605,
32316,
45252,
895... | [
0.07012939453125,
0.050048828125,
0.120361328125,
0.0723876953125,
0.0189971923828125,
0.1064453125,
0.09954833984375,
0.185546875,
0.188720703125,
0.09332275390625,
0.232421875,
0.2266845703125,
0.10455322265625,
0.064453125,
0.2108154296875,
0.019134521484375,
0.0391845703125,
0.... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.