robench-2024b
Collection
48 items • Updated
text_with_holes stringlengths 270 1.97k | text_candidates stringlengths 89 1.59k | A stringclasses 6
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We can apply the concepts of proper time oscillation outside quantum theory. If we neglect all quantum effects, a proper time oscillator can be treated as a ’stationary’ classical object, equivalent to a point mass at rest in general relativity. <|MaskedSetence|> <|MaskedSetence|> [6, 7]. The self-adjoint time opera... | **A**: Sections 3 and 4 provide an overview of a proper time oscillator’s quantum properties and gravitational field.
**B**: These results have been recently affirmed in refs.
**C**: Under this assumption, we expect the proper time oscillator to curve the surrounding spacetime and generate a gravitational field; its ... | CBA | CBA | CBA | ABC | Selection 3 |
<|MaskedSetence|> Typically, in this context one assumes that weakly interacting bosons occupying different wells can be described with two independent single-particle orbitals and that the dynamics is governed by two mechanisms: contact two-body interactions acting locally and single-particle tunneling between wells.... | **A**:
In view of recent experimental progress with ultra-cold atoms forming a Bose-Einstein condensate, double-well systems are one of the most commonly exploited schemes studied Andrews ; Smerzi ; Milburn ; Menotti ; Meier ; Shin ; Albiez ; Levy ; Salgueiro ; Simon ; Liu .
**B**: Although the validity of these sim... | ABC | ABC | CBA | ABC | Selection 2 |
<|MaskedSetence|> Realizing Harmonic Oscillators With Coupled Supersymmetry
As previously noted, the quantum mechanical harmonic oscillator is a specific instance of a coupled supersymmetry, albeit a somewhat trivial case in which the two coupled SUSY equations are identical. This is not the only manner in which the ... | **A**: they satisfy the same Lie algebra and by virtue of Stone-von Neumann, may be realized in some way as harmonic oscillators.
**B**:
7.
**C**: If one takes γ=−δ𝛾𝛿\gamma=-\deltaitalic_γ = - italic_δ, then the coupled SUSY equations become
.
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unstable again however in a reversed way: unlike an ordinary matter
ball it performs an unbounded contraction. <|MaskedSetence|> E<0𝐸0E<0italic_E < 0 and is
already small i.e. 0<Rinitial<−Gm2/2E0subscript𝑅initial𝐺superscript𝑚22𝐸0<R_{\rm initial}<-Gm^{2}/2E0 < italic_R start_POSTSUBSCRIPT roman_initial end_POSTS... | **A**: Applying (7)
we find again that R→0→𝑅0R\rightarrow 0italic_R → 0 i.e.
**B**: a sufficiently small bounded.
**C**: The second possibility is
that the ball is gravitationally bounded i.e.
| BAC | CAB | CAB | CAB | Selection 2 |
fails, in the sense that there can be no such simple decomposition as the group associated to the bulk space will include also a de-Sitter component. However, it is still possible to reconstruct a boundary theory by carefully restricting the doubled coordinates in the bulk region close to the boundary. There are sever... | **A**: Also, effects associated to the extended nature of the strings, from where double field theory extracts its stranger features, seem to be related to mixing of operators in the boundary and to a left-right symmetry which should not otherwise be present [46].
.
**B**: Heuristically speaking, it is possible to i... | CBA | CBA | CBA | CBA | Selection 3 |
<|MaskedSetence|> The calculation presented here relies on properties of the exterior family of metrics. <|MaskedSetence|> It is not clear if one could define some timescale analogous to T𝑇Titalic_T that would have a meaning for an arbitrary exterior spacetime, therefore rendering the entire calculation not applicab... | **A**: It can be noted that it is not obvious to us how to do such a comparison in the first place, at least with the techniques we used here.
**B**: Indeed, as we have seen in Section III.5 here T𝑇Titalic_T is best thought of as a parameter of the specific exterior geometry we consider.
**C**: We have considered th... | ACB | ACB | BCA | ACB | Selection 4 |
Let (Co,q→o)subscript𝐶𝑜subscript→𝑞𝑜(C_{o},\vec{q}_{o})( italic_C start_POSTSUBSCRIPT italic_o end_POSTSUBSCRIPT , over→ start_ARG italic_q end_ARG start_POSTSUBSCRIPT italic_o end_POSTSUBSCRIPT ) be a s𝑠sitalic_s-pointed ΓΓ\Gammaroman_Γ-curve such that ΓΓ\Gammaroman_Γ acts stably on Cosubscript𝐶𝑜C_{o}italic_C ... | **A**: Let z′superscript𝑧′z^{\prime}italic_z start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT (resp.
**B**: r′′superscript𝑟′′r^{\prime\prime}italic_r start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT) for the curve C~osubscript~𝐶𝑜\tilde{C}_{o}over~ start_ARG italic_C end_ARG start_POSTSUBSCRIPT italic_o end_POSTSUBSCRIPT. ... | ACB | ACB | ACB | ABC | Selection 1 |
A pseudo-species is not a single type of anyons. Rather, the single-particle states of a pseudo-species correspond to different types of anyons (see Fig. 6).
This also answers the question 2) raised in the second paragraph in the introduction Section 1. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> | **A**: 4(e), a subsystem of any number of real anyons is characterized by the pseudo-species; the observables associated with the pseudo-species supply good quantum numbers (topological charges) of the subsystem.
**B**: Seen in Fig.
**C**: The single-particle states of the pseudo-species are precisely these topologic... | BCA | BAC | BAC | BAC | Selection 3 |
<|MaskedSetence|> The paper is organized as follows. <|MaskedSetence|> In Section 3, we give a concise example for the MSR of the mixed-spin (1/2,1/2)1212(1/2,1/2)( 1 / 2 , 1 / 2 ) systems. <|MaskedSetence|> A brief discussion and summary are given in Section 5.
. | **A**:
Our study provides an intuitive perspective of a two-spin (s𝑠sitalic_s and 1/2121/21 / 2) system and unveils the intrinsic property of the two-spin system on a Bloch sphere, which shall deepen our comprehension of the spin-(s,1/2)𝑠12(s,1/2)( italic_s , 1 / 2 ) system.
**B**: In Section 2, we study the fundam... | CAB | ABC | ABC | ABC | Selection 3 |
<|MaskedSetence|> italic_e . <|MaskedSetence|> Similarly, the
element-to-node divergence operator produces valid results at the
boundary nodes only if the original continuous function 𝐩𝐩\mathbf{p}bold_p
has no component perpendicular to the boundary (i.e.,𝐩⟂|Γ=0)(i.e.,\,\mathbf{p_{\perp}}|_{\Gamma}=0)( italic_i . ... | **A**: is zero at the boundary (i.e.,u|Γ=0)(i.e.,\,u|_{\Gamma}=0)( italic_i .
**B**: , bold_p start_POSTSUBSCRIPT ⟂ end_POSTSUBSCRIPT | start_POSTSUBSCRIPT roman_Γ end_POSTSUBSCRIPT = 0 ).
In the following, we will refer to these conditions as the natural.
**C**: , italic_u | start_POSTSUBSCRIPT roman_Γ end_POSTSUBSC... | ACB | ACB | CAB | ACB | Selection 4 |
Since our identification will use a certain set of (framed) wild harmonic bundles, we remark that this set does not match any of the usual wild moduli spaces ℳHitsubscriptℳHit\mathcal{M}_{\text{Hit}}caligraphic_M start_POSTSUBSCRIPT Hit end_POSTSUBSCRIPT. In the usual story of moduli spaces of wild harmonic bundles o... | **A**: Under certain stability conditions, one obtains moduli spaces of these objects, with the natural hyperkähler metric [BB04].
**B**: Furthermore, we will have the additional data of a “framing”.
**C**: On the other hand, in our set of wild harmonic bundles we will allow the simple pole of the Higgs field and the... | ACB | ACB | ACB | BCA | Selection 1 |
<|MaskedSetence|> During the first two solar encounters, the reported AC power spectra are the mean of 16 individual power spectra calculated during the first 1/8 of each New York second (NYs = 217superscript2172^{17}2 start_POSTSUPERSCRIPT 17 end_POSTSUPERSCRIPT / 150,000 ≈\approx≈ 0.874 s (Bale et al., 2016)). <|Ma... | **A**:
This study utilizes power spectra calculated on-board by the FIELDS Digital Fields Board (DFB) (Malaspina et al., 2016).
**B**: AC power spectra are calculated for 4 channels.
**C**: For the first solar encounter, these channels were V12subscript𝑉12V_{12}italic_V start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT and... | ABC | ABC | ABC | BCA | Selection 2 |
made non-negative (i.e. only zero in this case) for a single choice of
parameters. <|MaskedSetence|> <|MaskedSetence|> The both cases yield an isolated root ±12(1−𝐞3+𝐞12+𝐞123)plus-or-minus121subscript𝐞3subscript𝐞12subscript𝐞123\pm\frac{1}{2}(1-\mathbf{e}_{3}+\mathbf{e}_{12}+\mathbf{e}_{123})± divide start_ARG ... | **A**: Alternatively, in the case s2=−12subscript𝑠212s_{2}=-\tfrac{1}{2}italic_s start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = - divide start_ARG 1 end_ARG start_ARG 2 end_ARG from
equation −4V22−(1−2V3)≥04superscriptsubscript𝑉2212subscript𝑉30-4V_{2}^{2}-(1-2V_{3})\geq 0- 4 italic_V start_POSTSUBSCRIPT 2 end_POSTSUBSC... | CAB | CAB | ACB | CAB | Selection 2 |
<|MaskedSetence|> <|MaskedSetence|> Before classifying an unlabeled sample, the recurrent pathway processes a sequence of labeled samples from the preceding batches to generate a context representation, which is fed into the skill processing layer. <|MaskedSetence|> The context system thus transforms samples of rece... | **A**:
III-C2 The context+skill model
The context+skill NN model builds on the skill NN model by adding a recurrent processing pathway (Fig.
**B**: The recurrent layers are modified via backpropagation through time, and, in this manner, the recurrent pathway learns to generate representations that support classific... | ACB | ACB | CAB | ACB | Selection 4 |
It is well known that there are close relations between entanglement and spin squeezing, and a lot of effort has been devoted to unveiling it Ulam-Orgikh and Kitagawa (2001); Jin and Kim (2007); Jafarpour and Akhound (2008); Messikh et al. (2003); Wang (2004); Yin et al. (2010).
Because spin squeezing is relatively eas... | **A**: (2003); Fernholz et al.
**B**: (2009), spin-squeezing parameters are promising candidates as measures of many-body correlations.
Improving the precision of measurements is another important application of spin squeezing.
For example, spin squeezing plays an important role in Ramsey spectroscopy Wineland et al. ... | ABC | ABC | ABC | BAC | Selection 1 |
<|MaskedSetence|> Acknowledgements
During the writing of the paper, I was supported by the starter grant “Categorified Donaldson–Thomas theory” No. <|MaskedSetence|> I was also supported by a Royal Society university research fellowship. <|MaskedSetence|> Finally, I offer my heartfelt gratitude to Paul, Sophia, Sac... | **A**: 759967 of the European Research Council.
**B**: I would like to thank Andrei Okounkov and Olivier Schiffmann for helpful conversations, Tristan Bozec for patiently explaining his work on crystals to me, Lucien Hennecart and Shivang Jindal for helpful comments regarding an earlier version of the paper, and an an... | CAB | CAB | CAB | BAC | Selection 1 |
The third study-case is the decay of Higgs to two Z𝑍Zitalic_Z bosons and their subsequent
decay into four leptons.
This final state has been extensively studied in the past as the golden decay mode of the Higgs boson and in searches for physics beyond the Standard Model Keung et al. <|MaskedSetence|> <|MaskedSetence... | **A**: (2010); Bolognesi et al.
**B**: (2016); Berge et al.
**C**: (2008); Gao et al.
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<|MaskedSetence|> <|MaskedSetence|> Diagrammatically defined chains of algebras appear to have not been considered as objects whose representation category can be studied through the lens of representation stability. Diagrammatics and representation stability have, however, been uttered in the same breadth, but in a ... | **A**: It appears that much of the work in representation stability has focussed on algebraic objects which are either close to symmetric groups [5] [14] [8] (Wilson, Putman, Sam, Gunturkun, Snowden ) or are close to Lie groups [14] [17] (Sam, Snowden, Putman).
**B**:
To our knowledge, Temperley-Lieb algebras have n... | CBA | BAC | BAC | BAC | Selection 4 |
Lemaître redshift formula, viz. 1+z=a−11𝑧superscript𝑎11+z=a^{-1}1 + italic_z = italic_a start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT. <|MaskedSetence|> <|MaskedSetence|> One such type of VSL exists in the form of
the velocity of light being dependent on the scale factor, e.g. <|MaskedSetence|> | **A**: We believe that
this is an oversight, however.
**B**: c∝a−ζproportional-to𝑐superscript𝑎𝜁c\propto a^{-\zeta}italic_c ∝ italic_a start_POSTSUPERSCRIPT - italic_ζ end_POSTSUPERSCRIPT,.
**C**: There are certain types of VSL in which
the classic Lemaître redshift formula is no longer applicable,
warranting a rev... | CBA | ACB | ACB | ACB | Selection 3 |
For N𝑁Nitalic_N particles in each shot, the SQL, also known as the shot-noise limit, can be surpassed by using quantum effects such as entanglement Bollinger et al. (1996); Monz et al. (2011) and squeezing Muessel et al. (2015), reaching the so-called Heisenberg limit (HL), in which the sensitivity exceeds the SQL by ... | **A**: (2015); Law et al.
**B**: (2012).
.
**C**: (1996); Holland and Burnett (1993); Munro et al.
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<|MaskedSetence|> Factoring has a low-complexity quantum algorithm due to Shor [1], while it is believed to have only high-complexity classical algorithms. <|MaskedSetence|> Unlike factoring, oracle problems do have some lower bound proof methods: the polynomial [8], hybrid [9] and adversary [10, 11] methods. For exa... | **A**: Rigorously proving complexity lower bounds is hard.
**B**:
Another advantage of oracles is the provability of limitations of computation.
**C**: It has a proven complexity lower bound in classical [12] as well as quantum [9, 8] circuits.
| BAC | BAC | CAB | BAC | Selection 2 |
Using this featurization approach (with 15 features) outperforms all benchmarking models (automatminer, in comparison, uses 200 features) even when a linear regression model is chosen, as seen in Figure 4a. <|MaskedSetence|> When a non-linear learning model is used (neural network or random forest model) the MAEs are ... | **A**: This performance improvement is due to the superior implementation of how we featurize our slabs rather than the machine learning model itself.
**B**: The learning curve trend for the random forest model suggests that increasing the dataset size (by a factor of ∼10similar-toabsent10\sim 10∼ 10) could further im... | ABC | ABC | CBA | ABC | Selection 4 |
<|MaskedSetence|> <|MaskedSetence|> However, the error on the fitted amplitude in zero field is nearly as large as the value itself. <|MaskedSetence|> Due to the weak signal, not all parameters were fitted simultaneously. The peak center and width show no visible dependence on the magnetic field, and we have thus fi... | **A**: We fitted the data using Gaussian peaks on a sloping background.
**B**: The intensity of the peak decreases with decreasing field, but a tiny signal may still be present at 2 K in zero field.
**C**: III Results
A selection of raw ND data is presented in Fig. 1 (a), showing a clear field-induced peak at 14.9 T... | CBA | CBA | CBA | CBA | Selection 2 |
Section V describes how to compute multivoice signals in the frequency domain. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> We conclude this section by showing how to combine multiple voices to construct the full frequency-domain EMRI waveform.
In Sec. VI, we present various important technical details de... | **A**: We review the standard SPA Fourier transform and show how by including an additional derivative of the frequency it is straightforward to correct this artifact.
**B**: However, because the evolution of certain voices is not monotonic, the “standard” SPA calculation can fail, introducing singular artifacts at mo... | CBA | BAC | CBA | CBA | Selection 1 |
3 CONCLUSION AND OUTLOOK
Thanks to the development of superconducting technology, MHz-level repetition-rate electron beam has come true. Seeded FELs have been proved to be convincing method to produce fully coherent EUV and soft X-ray radiation. However, limited by the average power of laser system today, seeded FEL ... | **A**: The mechanical layout of the proposed technique is close to the that of nominal seeded FELs and this provides excellent conditions for subsequent proof-of-principle demonstrations and technical applications.
**B**: The achievable average power at EUV and soft X-ray range reaches about one hundred watts with a r... | BAC | BAC | BAC | ACB | Selection 3 |
<|MaskedSetence|> Bekenstein:1973ur ; Hawking:1974sw the iconic work done by Witten, in Ref. Witten:1998zw , by using the new-found AdS/CFT correspondence, as proposed in Ref. <|MaskedSetence|> <|MaskedSetence|> Chamblin:1999tk ; Chamblin:1999hg studied the thermodynamic associated to a charged AdS black holes in ... | **A**:
A little bit more than twenty years after such studies in Refs.
**B**: Maldacena:1997re , relates the Hawking temperature achieved in a curved high-dimensional spacetime to the temperature of a super conformal Yang-Mills theory in a flat four-dimensional spacetime.
**C**: Soon after Witten’s work the authors... | ABC | ABC | BCA | ABC | Selection 1 |
<|MaskedSetence|> At the very beginning of the test, the Maxwell demon will accompany the qubit carrier, for example, photons entering Bob’s device without being detected. The demon then secretly gains access to a specific part of Bob’s device and tries to obtain information about the measurement setting. <|MaskedSet... | **A**:
Suppose that Alice chooses to collaborate with a Maxwell demon, and they make an agreement on the cheating strategy as follows.
**B**: There are two situations in which Bob settles down his choice of measurement settings.
**C**: The first one is to settle down many run choices before Alice sends the qubit an... | BCA | ABC | ABC | ABC | Selection 4 |
<|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> VI.Vidi.192.109). G.Q. thanks the support from Fundação para a Ciência e a Tecnologia (Portugal), namely through projects CEECIND/02474/2018 and project UIDB/50008/2020 and IT project QuantSat-PT. R.A. acknowledges support from the Doctoral Programme in the Physi... | **A**: The authors are especially grateful to Jens Siewert, Andreas Osterloh, Barbara Kraus, and Karol Życzkowski for stimulating conversations which led to formal proof of Proposition 2 while staying at Centro de Ciencias de Benasque Pedro Pascual.
**B**: A.B acknowledges support from the National Science Center unde... | CAB | ACB | CAB | CAB | Selection 1 |
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