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set of nearly degenerate excited states, with average energy \(E_{\alpha}\). This assumption is equivalent to saying that the spectral function associated with each term is dominated by a narrow peak at \(E_{\alpha}\). This significant approximation is reasonable because the correction to the density matrix is only use... | |
does not have the relevant states. Hence, the fluctuation is not represented in the density matrix and the new system block will not possess its relevant states for that fluctuation. Later, when the roles of system and environment are reversed, the relevant states again do not appear. In a 1D system with short range in... | |
* (14) D. J. Cleaver, C. M. Care, M. P. Allen, and M. P. Neal, Phys. Rev. E **54**, 559 (1996); D. Antypov and D. J. Cleaver, J. Chem. Phys. **120**, 10307 (2004).
* (15) All quantities are given in reduced units defined in terms of Lennard-Jones potential parameters \(\epsilon_{LJ}\) and \(\sigma_{LJ}\): length in uni... | |
# Dirac Cosmology and the Acceleration of the Contemporary Universe
Cheng-Gang Shao, Jianyong Shen, Bin Wang
wangb@fudan.edu.cn Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
Ru-Keng Su
rksu@fudan.ac.cn China Center of Advanced Science and Technology (World Laboratory) P.O. Box... | |
After introducing the term \(-b_{2}\alpha^{2}\) in our theory and fit the adjust parameter \(b_{2}\) by supernova data, we have calculated the physical quantities of \(\bar{G}(t)\), \(a(t)\), \(q(t)\), \(\rho_{r}(t)/\rho_{b}(t)\) by using the data of present epoch as the initial conditions. We have found that the resul... | |
cosmological scale, especially at the late time of the universe evolution s10 s11 . Though Einstein GR has been proved to be correct by many experiments such as the excess perihelion precession of Mercury, gravitational redshift etc. at the scales of local system, it probably needs to be modified in the cosmological sc... | |
we set
\[p_{\theta^{(1)}}=0\quad p_{\theta^{(2)}}=p_{\theta}\] (22)
Eq.(17)-Eq.(22) and the equation of scalar curvature
\[R=6[\frac{{\ddot{a}}}{a}+(\frac{{\dot{a}}}{a})^{2}]=6(\dot{H}+2H^{2})\] (23)
given by the flat Robertson-Walker metric form a complete set. In principle, we can solve the set of equations to fi... | |
looks like the character of the dark energy. If we take \(p_{\theta^{(2)}}=w_{\theta}\rho_{\theta^{(2)}}\) as the equation of state of addition creation, we show the parameter of the pressure-to-density of the addition creation \(w_{\theta}\) versus time \(t\) in Fig.8 and find \(w_{\theta}(t=0)=-0.83\) which is much s... | |
ts with other models, we have also calculated the ratio of the density of addition creation and find
\[\frac{{\rho_{\theta^{(2)}}}}{{\rho_{\theta^{(1)}}+\rho_{\theta^{(2)}}+\rho_{r} +\rho_{b}}}=\Omega_{\Lambda}=0.8\] (24)
and that of the density of matter (multiplication creation and normal matter) in our model reads... | |
Introduction
According to the Dirac's arguments, the large dimensionless numbers provided by atomic physics and astronomy of our universe are connected with each other s1 . These numbers include: (i) the ratio of the electric to the gravitational force between an electron and a proton \(a_{1}={\raise 3.01385pt\hbox{${... | |
2. case: \({\mathbf{1}}\in S\). (The case \(-{\mathbf{1}}\in S\) is analogous, so that we will omit it here.)
Again we choose \(n\) vectors from \(I_{p-1}\) and \(m=k-1-n\) vectors from \(-I_{p-1}\). We may assume these vectors are \(e_{1},\dots,e_{n},-e_{n+1},\dots,-e_{k-1}\). Set \(b=\frac{m-n+1}{p-k}\); note that \... | |
* [25] Milan Vlach, _Conditions for the existence of solutions of the three-dimensional planar transportation problem_, Discrete Appl. Math. **13** (1986), no. 1, 61-78.
* [26] Philip Wagreich, _The growth function of a discrete group_, Group actions and vector fields (Vancouver, B.C., 1981), Lecture Notes in Math., vo... | |
is introduced in the field theoretical description of the mechanical momentum-energy current as a "kinetic momentum-energy tensor" (Minkowski).5 Here \(\mu_{0}\) is the scalar mass density and \(u_{i}\) is the velocity vector. The term \(S_{i}S_{k}\) is obviously quite analogous, except that the current vector is repla... | |
# The Conservation Laws in the Field Theoretical Representation of Dirac's Theory1
Footnote 1: _Editorial note_: Published in Zeits. f. Phys. 57 (1929) 484–493, reprinted and translated in [3]. This is Nb. 3 in a series of four papers on relativistic quantum mechanics [1, 2, 3, 4] which are extensively discussed in a c... | |
one, for obviously there are still essential features missing. On the one hand, this is not at all conceivable on the basis of a linear system of equations and, on the other hand, these equations (just like the classical field equations) do not have regular "eigensolutions" of the kind which would give stationary energ... | |
also form the components of a tensor. It is expedient to apply a factor of \(-\frac{1}{2}\) and therefore we put:
\[T_{ik}=-\frac{1}{2}(Fj_{i}\overline{F}^{*})_{k},\] (15)
and
\[U_{ik}=-\frac{1}{2}(G\overline{j}_{i}\overline{G}^{*})_{k}.\] (16)
The zero divergence tensor, which we shall denote by \(W_{ik}\), is com... | |
Let us first consider the tensor (15). It can be written in vector analytical terms as follows:
\[T_{ik}=SF_{ik}-M\widetilde{F}_{ik}-\frac{1}{2}(S^{2}+M^{2})g_{ik}+(F_{i}^{\nu} F_{k\nu}-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}g_{ik}).\] (15')
The first two terms are antisymmetric, the others are symmetric.
The other tensor (... | |
where \(j_{\alpha}\) stands for one of the four quaternion units.
The fact that the Dirac divergence equation is quadrupled here suggests that we have a vectorial divergence instead of a scalar one. If this is true, then the set of the four quaternions (5) should be equivalent to a tensor. In actual fact, this is the ... | |
Footnote 7: Although the electron is, of course, “smeared,” an estimate of the dimensions may be of interest for a comparison with electron theory. Let us consider a spherical shell of radius \(a\) with evenly distributed charge and mass. Then the hydrostatic pressure connected with the mass density \({M}/{4\pi\alpha^{... | |
have:
\[U_{ik}=\alpha^{2}(\varphi_{i}\varphi_{k}-\frac{1}{2}\varphi_{\nu}\varphi^{\nu} g_{ik}).\] (24)
In the peripheral domain, where \(\alpha\) has practically become zero, the mechanical component drops out and only the customary electromagnetic stress-energy tensor remains. However, in the central domain (just wh... | |
Papers With Commentaries, **III** (North Carolina State University, Raleigh, 1998) pages 2-1206 to 2-1225; e-print arXiv:physics/0508013 available at http://arXiv.org/abs/physics/0508013.
* [4] C. Lanczos, _Dirac's wellenmechanische Theorie des Elektrons und ihre feldtheorische Ausgestaltung (Dirac's wave mechanical th... | |
is solved -- as the author realized in the meantime -- by a fact which allows a much larger perspective for the field theoretical description and seems to confirm the inherent validity of the whole development to a great extent.
Footnote 2: Zeits. f. Phys. **57** (1929) 447 and 474, 1929. (_Editorial note:_ Refs. [1] ... | |
terms have already been reduced to zero and the linear approximation is justified, one would not obtain potentials decreasing with \(1/r\), the potential behavior would rather be characterized by \({e^{-\alpha r}}/{r}\). Here \(\alpha\) is the strong attenuation constant which definitely contradicts experience since it... | |
Fermi energy and with the temperature [10]. The spectral function in finite nuclei has been estimated taking into account the local density and the neutron-proton asymmetry [18] and compared to experimental data. Thermodynamic properties of the asymmetric [19] and pure neutron nuclear matter [20] have been discussed. W... | |
# Spectral properties of nuclear matter
P. Bozek1
Institute of Nuclear Physics, PL-31-342 Cracow, Poland
Footnote 1: Electronic address : piotr.bozek@ifj.edu.pl
(October 12, 2023)
###### Abstract
We review self-consistent spectral methods for nuclear matter calculations. The in-medium \(T-\)matrix approach is co... | |
The result of the calculation with self-energy and vertex corrections is compared to the RPA result in Fig. 11. The collective mode in the density response has a large width in the full calculation. This corresponds to the coupling of the sound mode to multipair excitations giving rise to a finite decay width, even at ... | |
sides the Fermi energy (Fig. 5). The most interesting result of this first, and up to now unique, study is the observation of a strong reduction of the superfluid gap in the correlated nuclear matter as compared to results from a mean-field gap equation [24]. This effect was analyzed in details [26] and can be explaine... | |
tion is similar to the one particle-one hole response function. On the other hand, the isovector response is closer to the naive one-loop result, without vertex corrections.
To study the role of multipair configurations on the collective modes we increase the value of the Landau parameters. Within the Fermi liquid t... | |
* [20] P. Bozek, P. Czerski, Phys. Rev., **C66** (2002) 027301.
* [21] J. Bardeen, L. N. Cooper, J. R. Schrieffer, Phys. Rev., **108** (1957) 1175.
* [22] B. Vonderfecht, C. Gerhart, W. Dickhoff, A. Polls, A. Ramos, Phys. Lett., **B253** (1991) 1.
* [23] P. Bozek, Phys. Rev., **C65** (2002) 034327.
* [24] P. Bozek, Nuc... | |
## References
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* [4] L. Kadanoff, G. Baym, _Quantum Statistical Mechanics_, Bejamin, New York, 1962.
* [5] W. H. Dickhoff, Phys. Rev., **C58** (1998) ... | |
the \(T-\)matrix scheme at finite temperature was also obtained in [12].
At low temperatures two difficulties show up. The first one is related to the transition to superfluidity in cold nuclear matter. This effect can be taken into account quite naturally within suitably generalized \(T-\)matrix approaches. This is t... | |
of the ladder diagram summation to the superfluid phase. We discuss equations which allow for a simultaneous and consistent treatment of the short range nuclear interactions, the bound state formation (Cooper pairs) in the \(T\)-matrix and the superfluidity in nuclear matter. Model calculations have allowed us to estim... | |
not expect better results for the binding energy in the \(T-\)matrix approximation than in the standard \(G-\)matrix approach with higher order terms in the hole line-expansion [17]. However, the authors of ref. [16] claim that the \(T-\)matrix calculation, which does not take into account ring diagrams contribution, i... | |
evel of the self-energy, which in the \(\Phi-\)derivable \(T-\)matrix approximation must be taken self-consistently in the form (Fig 2)
\[\Sigma=TrTG\ .\] (3)
The self-consistency means that the nucleon propagators at all stages of the approximation are dressed by this self-energy. It requires an iterative procedur... | |
in the normal phase. At the same time it should describe the formation of the superfluid long-range order in the two-particle correlations. Such correlations appear as a singularity of the \(T\) matrix for \(T=T_{c}\) at the energy of twice the fermionic chemical potential. This corresponds to the formation of a two-fe... | |
n of the BS equation the response function in the correlated medium can be obtained from the diagram in Fig. 9
\[\Pi_{(ST)}=Tr\Gamma^{0}_{(ST)}G_{ph}\Gamma_{(ST)}\ ,\] (6)
\(\Gamma_{(ST)}\) is the in-medium vertex for the coupling in a given spin-isospin \((ST)\) channel. The exact form of the BS equation in the re... | |
ery small multipair contributions in most of the kinematical regions. Some differences can occur only when collective modes are present, as discussed latter.
The situation is very different for a more general form of the residual interaction.
The kernel of the BS equation depends very much on the isospin channel, e... | |
quasiparticles and gives them nontrivial spectral properties; nucleons propagate off the energy shell. The description of nuclear matter in the language of such dressed nucleons with a broad spectral function has been the subject of intensive studies in the last years.
## 2 In medium \(T\) matrix
The description of p... | |
interactions [31].
We take the interactions between the nucleons as a sum of a mean-field interaction that is based on the Gogny parameterization [32] and a residual interaction (scalar or isospin dependent). The isospin dependent residual interaction is obtained from the scalar one multiplying by the factor \(\frac{1... | |
# Can one predict DNA Transcription Start Sites by studying bubbles?
Titus S. van Erp\({}^{1,2}\), Santiago Cuesta-Lopez\({}^{2,3}\), Johannes-Geert Hagmann\({}^{1,2}\), and Michel Peyrard\({}^{2}\)
\(1\) Centre Europeen de Calcul Atomique et Moleculaire (CECAM)
\(2\) Laboratoire de Physique, Ecole Normale Superieur... | |
Footnote 1: In principle, MD suffers from the same problem that it allows for complete separation. As a consequence, very long MD simulations will always give erroneous results. To restrict the MD to the dsDNA one can use a bias potential that acts on \(y_{\rm min}=\textrm{MIN}[\{y_{i}\}]\). For instance, \(V^{\rm bias... | |
* (3) C. H. Choi _et al._, Nucl. Acid Res. **32**, 1584 (2004); G. Kalosakas _et al._, Eur. Phys. Lett. **68**, 127 (2004).
* (4) M. Peyrard and A. R. Bishop, Phys. Rev. Lett. **62**, 2755 (1989).
* (5) T. Dauxois, M. Peyrard, and A. R. Bishop, Phys. Rev. E **47**, 684 (1993).
* (6) A. Campa and A. Giansanti, Phys. Rev... | |
#### Atmospheric parameters
\(T_{\rm{eff}}\) uncertainties are the most important contributor to uncertainties in abundance for all elements except C and S (see below). To estimate a realistic \(T_{\rm eff}\) uncertainty we compare \(T_{\rm eff}\) derived from the spectroscopy with that derived using the relationship ... | |
# Elemental abundances in the Blanco 1 open cluster
A. Ford\({}^{1}\), R.D. Jeffries\({}^{2}\) and B. Smalley\({}^{2}\)
\({}^{1}\)CSPA/SPME, Building 28M, Monash University, VIC 3800, Australia
\({}^{2}\)Astrophysics Group, School of Chemistry and Physics, Keele University, Keele, Staffordshire ST5 5BG, United Kingd... | |
no major systematic uncertainties in the temperatures we have used and no problems with our ionization balance temperatures caused by possible NLTE overionization effects in the Fe ii lines - which may become more apparent in cooler stars (\(<5500\) K - see Schuler et al. 2003; Allende-Prieto et al. 2004). In addition ... | |
- which E95 discount as a cluster member on the basis of its abundance!) and W63 ([Fe/H]=E95+0.21+-0.01) - but in our analysis these stars are cooler by 225 K, 150 K and 420 K respectively. If E95 had adopted the atmospheric parameters we have used, then their [Fe/H] for W8 and W63 would have been in excellent agreemen... | |
# Selective advantage for multicellular replicative strategies: A two-cell example
Emmanuel Tannenbaum
etannenb@gmail.google.com Ben-Gurion University of the Negev, Be'er-Sheva, Israel 84105
###### Abstract
This paper develops a quasispecies model where cells can adopt a two-cell survival strategy. Within this stra... | |
portion of the genome coding for this strategy undergoes a localization to delocalization transition, analogous to the error catastrophe (it is also similar to a phenomenon known as "survival of the flattest") Tannenbaum and Shakhnovich (2005); Wilke (2001).
Figure 2 shows the various solution regimes as a function ... | |
cells in the replicating cell-pair has active reproductive pathways, the total energy consumption rate is given by \(2(\dot{\rho}-\Delta\dot{\rho})=\dot{\rho}_{R}+2\dot{\rho}_{M}+2\dot{\rho}_{S}\), where \(\Delta\dot{\rho}\equiv(1/2)(\dot{\rho}_{R}-2\dot{\rho}_{S})\). Therefore, the replication time is given by,
\[\ta... | |
implement the two-cell survival strategy is a switch that causes one of the cells to shut off its reproductive pathways, and to devote itself to metabolizing food from the environment for the sake of the other cell. This part of the genome is denoted by \(\sigma_{S}\).
The full cellular genome is denoted by \(\sigma=\... | |
Plaquette formulation and expression for the Jacobian
In this section we give our formulation of the plaquette representation for \(3D\)\(SU(N)\) LGT. A short description of our procedure can be found in [22] for pure gauge theory and in [23] for a theory with fermions. In subsection 2.1 we calculate the plaquette rep... | |
**Plaquette representation for \(3D\) lattice gauge models: I. Formulation and perturbation theory**
**O. Borisenko1, S. Voloshin2**
Footnote 1: email: oleg@bitp.kiev.ua
Footnote 2: email: sun-burn@yandex.ru
_N.N.Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, 03143 Kiev, Ukra... | |
partition function) for every cube and goes towards gradual restoration of the full identity with every order of the expansion. Thus, the generating functional contains an abelianized form of the identity without connectors. High-order terms include expansion of connectors (of course, together with other contributions ... | |
.
* [25] G. Batrouni, M.B. Halpern, Phys.Rev. D30 (1984) 1775.
* [26] V.F. Muller, W. Ruhl, Ann.Phys. 133 (1981) 240.
* [27] O. Borisenko, S. Voloshin, M. Faber, Plaquette representation for \(3D\) lattice gauge models: II. Dual form and its properties, in preparation. | |
identical, while the only (but essential) difference in the non-abelian gauge models is the appearance of connectors.
A lattice PT in the maximal axial gauge was constructed for abelian and non-abelian models in the standard Wilson formulation by F. Muller and W. Ruhl in [26]. In this gauge the PT for non-abelian mode... | |
and then expand the integrand of (63) in powers of fluctuations of the link fields. We introduce now the external sources \(h_{k}(l)\) coupled to the link field \(\omega_{k}(l)\) and \(s_{k}(x)\) coupled to the auxiliary field \(\alpha_{k}(x)\) and adopt the definitions
\[\omega_{k}(l)\to\frac{\partial}{\partial h_{k}... | |
problem of the standard perturbation theory (PT), i.e. whether PT is uniformly valid in the volume, can be shortly formulated in the following way. When the volume is fixed, and in the maximal axial gauge the link matrices perform small fluctuations around the unit matrix and the PT works very well producing the asympt... | |
ollowing manner. Connectors generate contributions of the form \(\sum_{l\in C}\omega_{k}(l)\) and of high order to all \(\omega_{k}^{(i)}(x)\), see Eqs.(100), (105)-(107). And though all \(\omega_{k}(l)\) behave like \({\cal O}(1/\sqrt{\beta})\) it is not obvious if it remains true for the sums of the plaquette angles ... | |
local interaction. Let \(H[U]\) be a real invariant function on \(G\) such that
\[\mid H[U]\mid\ \leq H(I)\] (5)
for all \(U\) and coefficients of the character expansion of \(\exp(\beta H)\)
\[C[r]\ =\ \int DU\ \exp\left(\beta H[U]\right)\chi_{r}(U)\] (6)
exist. Introduce the plaquette matrix as
\[V_{p}\:=\:U_{n}... | |
the Wilson LGT contrary to the claim of [17]. Exact calculations on a \(3^{3}\) lattice show the equivalence between Wilson LGT and the model of [17] but the equivalence is lost already for a \(4\times 3^{2}\) lattice. The point is that the constraints on the plaquette matrices in the model of [17] do not match the non... | |
* [6] I. Halliday, P. Suranyi, Phys.Lett. B350 (1995) 189.
* [7] R. Oeckl, H. Pfeiffer, Nucl.Phys. B598 (2001) 400-426.
* [8] D. Diakonov, V. Petrov, Journal Exp. Theor. Phys. 91 (2000) 873-893.
* [9] O. Borisenko, M. Faber, Dual representation for lattice gauge models, Proc. of the International School-Conference "New... | |
(7) in the partition function (13). Then the partition function gets the form
\[Z_{\Lambda}(\beta,m_{f},N_{f})=\int\prod_{p}dV_{p}\exp\left\{\beta\sum_{p\in \Lambda}H[V_{p}]\right\}\prod_{p}\ J(V_{p})\ ,\] (16)
where the Jacobian of the transformation reads
\[J(V_{p})\:=\:\int\prod_{l}dU_{l}\ \prod_{p}\delta\left(V_... | |
variables which label the irreducible representations of the underlying gauge group and can be written solely in terms of group invariant objects like the \(6j\)-symbols, etc. A closely related approach to the dual formulation is the so-called plaquette representation invented originally in the continuum theory by M. H... | |
only a rough estimate, nevertheless, qualitatively it is true and shows that large fluctuations are under good control since they are exponentially suppressed with \(\beta\), and this obviously remains true in the TL. As we have already stressed, this property is an essential achievement of the expansion in the plaquet... | |
easure. For the partition function we expect up to a constant factor an expression of the form
\[Z=1+\sum_{k=1}^{\infty}\frac{1}{\beta^{k}}\langle B_{k}\rangle_{G}\ .\] (57)
Let us consider the standard parameterisation for the \(SU(2)\) link matrix
\[V_{l}=\exp[i\sigma^{k}\omega_{k}(l)]\ ,\] (58)
where \(\sigma^{k... | |
# Optimizing photon indistinguishability in the emission from incoherently-excited semiconductor quantum dots
F. Troiani
filippo.troiani@uam.es Departamento de Fisica Teorica de la Materia Condensada, Universidad Autonoma de Madrid, 28049 Madrid, Spain
J. I. Perea
Departamento de Fisica Teorica de la Materia Conden... | |
incidence probabilities between the \(\gamma\neq 0\) and the \(\gamma=0\) cases occurs in the slow-emission region; the values of \(R\) at which the two values approach each other grow with increasing dephasing rate. However, the curves corresponding to different values of \(\gamma\) are not similar, i.e. they don't re... | |
* (4) F. De Martini, G. Di Giuseppe, and M. Marrocco, Phys. Rev. Lett. **76**, 900 (1996); C. Brunel _et al._, Phys. Rev. Lett. **83**, 2722 (1999); B. Lounis, and W.E. Moerner, Nature (London) **407**, 491 (2000).
* (5) C. Santori _et al._, Nature (London) **419**, 594 (2002).
* (6) P. Michler _et al._, Science **290*... | |
term is to be
\[\frac{1}{6}\int_{Z^{12}}G_{4}\wedge G_{4}\wedge G_{4},\] (2)
but one must adjust the expression so that it doesn't depend on the choice of the spin cobordism \(Z^{12}\). In particular, we want to get \(0\) on a closed \(12\)-manifold \(Z^{12}\). It turns out ([11]) that the corrected expression is
\[... | |
# Some remarks on fundamental physical F-theory
Igor Kriz
The author is supported by NSF grant DMS 0305853
###### Abstract
The purpose of this paper is to investigate the possibility of a physical 12-dimensional F-theory. We study the question of geometric interaction terms in the F-theory Lagrangians. We also intr... | |
up with \(64/8=8\) supercharges, which form the total spin representation of \(Spin(6)\) (there are two complex conjugate \(4\)-dimensional half-spin representations, which however do not possess a real structure). Thus, the shortest supermultiplet is therefore just has \(2^{4}\) elements.
Let us now look at the short... | |
into a triplet of dimensions". This scenario is _only possible_ in signature \((9,3)\). To confirm the the theory we present here, one needs more precise calculation of \((9,3)\)-SUGRA dynamics, although we have reconstructed a substantial part of its action from the effective low energy action of F-theory. Another imp... | |
will see below that there is in fact a tie between \(G_{4}\) and \(G_{5}\), although not exactly in the form of an equation.
We made further progress on answering these questions in [5]. The purpose of that paper was to derive an analogue of [12], which would match the elliptic partition function on \(X^{10}\) of type... | |
world volumes of dimension \((2k-1,1)\) in type IIA, we have branes which are world volumes of dimension \((2k,0)\), i.e. time instantons.
Hull continues to examine the theory \(\text{IIA}^{*}\), in particular its strong coupling limit. He concludes that although the strong coupling limit is \(11\)-dimensional, becaus... | |
In [5], we also noted that there should be another "self-T-duality" of the fibered \(F\)-theory. Consider F-theory on
\[X^{9}\times\begin{array}[]{c}{ 3}\\ \prod\\ { i=1}\end{array}S^{1}_{R}\] (20)
which is a special case of (19). Then this theory should have a \(2\)-brane \(M_{2}\) and a \(3\)-brane \(M_{3}\) where ... | |
is a spin-cobordism of the spacetime of M-theory. On the other hand, in the context of IIB string theory, we expect \(Z^{12}\) to be a closed \(12\)-manifold which is elliptically fibered over \(X^{10}\). Yet, these theories should be in a string duality which would lift the T-duality between type IIA and IIB. How is t... | |
there is indeed an approximate relation among the three dimensions in a triplet (from an observation point of view, this is particularly important in the time dimensions). One mechanism which could explain this is that the theory in fact has a \(3\)-brane with one time-like dimension (corresponding to the potential \(A... | |
Next thing we considered in [5] was how the F-theory on a cobordism of M-theory spacetime and F-theory elliptically fibered on IIB spacetime could be related by duality. We proposed, in fact, such a process: in the case of IIA spacetime \(X^{9}\times S^{1}\) subject to T-duality, we obtain M-theory on \(X^{9}\times S^{... | |
summands constitute the real gravitino representation, as predicted by the general formula.
The bosonic content may be more surprising: we have
\[(V\otimes M)_{b}=\mathbf{6}+\mathbf{6}+\mathbf{1}+\mathbf{15}+\mathbf{20}.\] (15)
Therefore, we have a scalar (dilaton) and two vectors, the graviton \(\mathbf{20}\) and a... | |
nomenology. It is possible that instead of splitting spacetime as a direct sum where excess dimensions are "discarded", a \((9,3)\)-dimensional space could in fact be represented as a tensor product, where one factor is phenomenological spacetime. Confinement using the \(3\)-brane in F-theory wrapped around a topologic... | |
constructed F-theory of signature \((9,3)\) fibered over IIB of signature \((9,1)\) by a time-like elliptic curve.
Let us now briefly examine branes in this setting, and try to match them to the supergravity sources (15). Specifically, let us notice that type \(\text{IIA}^{*}\) has a \((3,0)\)-signature world volume. ... | |
strength which is the natural extension of the \(K\)-theory field strength considered there (see also [13]) violates S-duality of type IIB. The author and Sati [3, 4] in fact showed that this cannot be remedied simply by modifying the definition of twisted K-theory without introducing other fields. Their investigation ... | |
For now, however, let us remark that while exploring that connection, another piece of the picture emerged: to define the elliptic partition function, a \(4\)-dimensional obstruction showed up, which is of a similar nature as obstructions in type I and heterotic string theory. This was our first suggestion that there s... | |
independent, and only tied by the assumption that they correspond to a joint field strength on loop space:
\[(G_{4},G_{5})=G\in H^{4}(LZ^{12},\mathbb{Z}).\] (9)
This is consistent with the interpretation of the \(4\) and \(5\)-dimensional field strength being explained by a \(3\)-brane moving in the loop space. Note ... | |
The purpose of this paper is to investigate these questions and to show new indications that a fundamental F-theory, in fact, does exist, while exploring how that would be possible and what it would imply. The first motivation of this project was a previous joint investigation with Sati [2, 3, 4], where we discovered e... | |
* [25] B.De Wit, J. Louis: _Supersymmetry and dualities in various dimensions_, Proc. NATO Advanced Study Institute on "Strings, Branes and Dualities", Cargese, May 26-June 4, 1997, eds. L. Baulieu, P. DiFrancesco, M.Douglas, V.Kazakov, M.Picco and P.Windey, NATO ASI C520 Kluwer Ac. Publ. 1999, 33-101, [arXiv:hep-th/98... | |
where \(S_{\ell}\) is the Eisenstein series
\[S_{\ell}=S_{\ell}(\tau)=-\frac{B_{\ell}}{2{\ell}}+\begin{array}[]{c}{ \infty}\\ \sum\\ { n=1}\end{array}\left(\begin{array}[]{c}\\ \sum\\ { d|n}\end{array}d^{\ell-1}\right)q^{n}.\] (8)
Now we matched in [5] the resulting 'phase term' with the phase factor of a variant of ... | |
Possible phenomenological predictions of \(F\)-theory in signature \((9,3)\)
One intriguing aspect of the scenario described above, i.e. a \((9,3)\)-dimensional supergravity based on a massless particle with three time dimensions being the low energy limit of signature \((9,3)\) F-theory, is that it offers a possible ... | |
[11] E. Witten, _On flux quantization in M-theory and the effective action_, J. Geom. Phys. **22** (1997) 1, [arXiv:hep-th/9609122]
* [12] E. Diaconescu, G. Moore and E. Witten, \(E_{8}\) _gauge theory, and a derivation of K-Theory from M-Theory_, Adv. Theor. Math. Phys. **6** (2003) 1031, [arXiv:hep-th/0005090]
* [13]... | |
# Transverse tunneling current through guanine traps in DNA
Vadim Apalkov\({}^{\ast{\dagger}}\) and Tapash Chakraborty\({}^{\ast{\ddagger}}\)
\({}^{\ast}\)Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2 \({}^{\dagger}\)Department of Physics and Astronomy, Georgia State University... | |
illustrated in Figs. 1 (b,d) by a black line for \(\gamma=0.1\) and \(\gamma=0.2\). With increasing gate voltage the phonon steps disappear and the I-V curve shows a clear two-step structure. The origin of such a suppression of phonon steps is the following. If the relaxation time is much smaller than the tunneling tim... | |
leads, and \(f_{\alpha}(\epsilon)\) is the Fermi function of the lead \(\alpha\) with a chemical potential \(\mu_{\alpha}\).
For the stationary case the time derivatives of \(P_{1,n}\) and \(P_{0,m}\) are zero and Eqs. (5)-(6) becomes the system of linear equations with condition of normalization \(\sum_{n}P_{1,n}+\... | |
port. Whether it is a hole transport or electron transport depends on the gate potential, i.e. on the position of the chemical potential at zero source-drain voltage \(V_{sd}\).
We disregard below the effects related to a Coulomb blockade coulomb or to a double occupancy of the DNA traps, assuming that the repulsion b... | |
# Pseudo-Hermiticity, \({\cal PT}\)-symmetry,
and the Metric Operator1
Footnote 1: Contributed to the Proceedings of the 3rd International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics, June 20-22, 2005, Koç University, Istanbul, Turkey.
Ali Mostafazadeh
Department of Mathematics, Koc University,
344... | |
approach as in the first method mentioned above. A variation of the second perturbative method is introduced in [16]. But because the authors confine their attention to the \({\cal CPT}\)-inner product they miss a large class of alternative and equivalently admissible positive-definite metric operators (inner products)... | |
## References
* [1] A. Mostafazadeh, J. Math. Phys. **43**, 205 (2002)
* [2] A. Mostafazadeh, Czech J. Phys. **53**, 1079 (2003) and referenes therein
* [3] A. Mostafazadeh, Phys. Lett. A **264**, 11 (1999)
* [4] A. Mostafazadeh, J. Math. Phys. **39**, 4499 (1998)
* [5] A. Mostafazadeh, J. Math. Phys. **43**, 2814 (20... | |
# Quantum search algorithm as an open system
A. Romanelli
A. Auyuanet
and R. Donangelo
Instituto de Fisica, Facultad de Ingenieria
Universidad de la Republica
C.C. 30, C.P. 11000, Montevideo, Uruguay
(October 11, 2023)
###### Abstract
We analyze the responses of a quantum search algorithm to an external monoch... | |
where \(\omega_{nm}=\varepsilon_{m}-\varepsilon_{n}\) are Bohr frequencies. Inserting the definitions (1) and (4) into (5), we find,
\[\frac{da_{n}(t)}{dt}=-i\sin\omega_{0}t\ \sum_{m}\Gamma_{nm}a_{m}(t)\exp\left(- i\omega_{nm}t\right)\,,\] (6)
for \(n\notin\mathbf{N}\) and \(n\neq j\), and
\[\frac{da_{n}(t)}{dt} =-\... | |
\[a_{j}(t) =x_{j}(t)\exp\left[i\Gamma_{jj}\left(\cos\omega_{0}t-1\right)/ \omega_{0}\right],\] \[a_{s}(t) =x_{s}(t)\exp\left[i\Gamma_{ss}\left(\cos\omega_{0}t-1\right)/ \omega_{0}\right],\] (9)
in those equations, we obtain
\[\frac{dx_{j}(t)}{dt} =-i\text{ }\Omega\text{ }x_{s}(t)\exp\left[i\varepsilon\left(\cos \omeg... | |
for the searched and initial states were obtained analytically. When a set of periodic measurements are performed, the probability distribution satisfies a Master equation. In this way we have shown that the global behavior of the algorithm becomes a Markovian process. Therefore, the algorithm can still be useful in th... |
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