Date: Wed, 30 Oct 13 00:18:50 GMT Subject: math-ph daily 7 new + 7 crosses received by eprepget ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Send any comments regarding submissions directly to submitter. ------------------------------------------------------------------------------ Archives at http://arxiv.org/ To unsubscribe, e-mail To: math-ph@arXiv.org, Subject: cancel ------------------------------------------------------------------------------ received by eprepget from Mon 28 Oct 13 20:00:00 GMT to Tue 29 Oct 13 20:00:00 GMT ------------------------------------------------------------------------------ \\ arXiv:1310.7615 Date: Mon, 28 Oct 2013 20:40:56 GMT (186kb) Title: Rescaled Magnetization for Critical Bipartite Mean-Fields Models Authors: Micaela Fedele Categories: math-ph math.MP Comments: 20 pages, 1 figure \\ We consider a bipartite generalization of the Curie-Weiss model in a critical regime. In order to study the asymptotic behavior of the random vector of the total magnetization we apply the change of variables that diagonalizes the Hessian matrix of the pressure functional associated to the model. We obtain a new vector that, suitably rescaled, weakly converges to the product of a Gaussian distribution and a distribution proportional to $\exp(-\xi x^{4})$, where the positive constant $\xi$ can be computed from the pressure functional. \\ ( http://arxiv.org/abs/1310.7615 , 186kb) ------------------------------------------------------------------------------ \\ arXiv:1310.7700 Date: Tue, 29 Oct 2013 07:51:31 GMT (11kb) Title: Epsilon expansion of Appell and Kamp\'e de F\'eriet functions Authors: David Greynat, Javier Sesma and Gr\'egory Vulvert Categories: math-ph hep-ph hep-th math.MP Comments: 18 pages \\ The decomposition in partial fractions of the quotient of Pochhammer symbols improves considerably a method, suggested in a precedent paper, which allows one to obtain the $\varepsilon$-expansion of functions of the hypergeometric class. The procedure is applied to several Appell and Kamp\'e de F\'eriet functions considered in the literature. Explicit expressions and interesting properties of the derivatives of the Pochhammer and reciprocal Pochhammer symbols, which are essential elements in the procedure, are given in an appendix. \\ ( http://arxiv.org/abs/1310.7700 , 11kb) ------------------------------------------------------------------------------ \\ arXiv:1310.7767 Date: Tue, 29 Oct 2013 11:46:45 GMT (13kb) Title: The real spectrum of the imaginary cubic oscillator: An expository proof Authors: Ilario Giordanelli, Gian Michele Graf Categories: math-ph math.MP Comments: 12 pages, 2 figures MSC-class: 81Q12 (Primary) 34L20, 34L40 (Secondary) \\ We give a partially alternate proof of the reality of the spectrum of the imaginary cubic oscillator in quantum mechanics. \\ ( http://arxiv.org/abs/1310.7767 , 13kb) ------------------------------------------------------------------------------ \\ arXiv:1310.7825 Date: Tue, 29 Oct 2013 15:08:41 GMT (12kb) Title: Quantifying Networks Complexity from Information Geometry Viewpoint Authors: Domenico Felice, Stefano Mancini and Marco Pettini Categories: math-ph math.MP Comments: 15 pages, 2 tables \\ We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as weighted edges among vertices. We then associate to the parameter space a statistical manifold endowed with a Riemannian metric structure (that of Fisher-Rao). Going on, in analogy with the microcanonical definition of entropy in Statistical Mechanics, we introduce an entropic measure of networks complexity. We prove that it is invariant under networks isomorphism. Above all, considering networks as simplicial complexes, we evaluate this entropy on simplexes and find that it monotonically increases with their dimension. This is a clear indication that such a definition is meaningful. \\ ( http://arxiv.org/abs/1310.7825 , 12kb) ------------------------------------------------------------------------------ \\ arXiv:1310.7835 Date: Tue, 29 Oct 2013 15:22:14 GMT (20kb) Title: Change of variables as a method to study general $\beta$-models: bulk universality Authors: Mariya Shcherbina Categories: math-ph math.MP Comments: 20 pages MSC-class: 15B52 \\ We consider $\beta$ matrix models with real analytic potentials. Assuming that the corresponding equilibrium density $\rho$ has a one-interval support (without loss of generality $\sigma=[-2,2]$), we study the transformation of the correlation functions after the change of variables $\lambda_i\to\zeta(\lambda_i)$ with $\zeta(\lambda)$ chosen from the equation $\zeta'(\lambda)\rho(\zeta(\lambda))=\rho_{sc}(\lambda)$, where $\rho_{sc}(\lambda)$ is the standard semicircle density. This gives us the "deformed" $\beta$-model which has an additional "interaction" term. Standard transformation with the Gaussian integral allows us to show that the "deformed" $\beta$-model may be reduced to the standard Gaussian $\beta$-model with a small perturbation $n^{-1}h(\lambda)$. This reduces most of the problems of local and global regimes for $\beta$-models to the corresponding problems for the Gaussian $\beta$-model with a small perturbation. In the present paper we prove the bulk universality of local eigenvalue statistics for both one-cut and multi-cut cases. \\ ( http://arxiv.org/abs/1310.7835 , 20kb) ------------------------------------------------------------------------------ \\ arXiv:1310.7882 Date: Tue, 29 Oct 2013 17:08:06 GMT (60kb,D) Title: Localized Quantum States Authors: Francois Ziegler Categories: math-ph math.MP math.RT math.SG Comments: 21 pages, 1 figure MSC-class: 53D50, 22E27, 22E45 \\ We investigate the notion of \emph{quantum representation}, introduced in the 1990's by J.-M. Souriau in an attempt to give a polarization-independent characterization of the unitary representations "attached" to coadjoint orbits of Lie and diffeological groups. Restricting attention to Lie groups, we show that Souriau's notion is far from selective enough due to a certain compactification implicit in the Definition. Yet the notion allows interesting, often \emph{discontinuous} representations which solve Weinstein's problem of attaching state vectors to lagrangian submanifolds. We show that these constitute a manageable class which can be characterized by a simple axiom. \\ ( http://arxiv.org/abs/1310.7882 , 60kb) ------------------------------------------------------------------------------ \\ arXiv:1310.7930 Date: Tue, 29 Oct 2013 19:40:51 GMT (788kb) Title: Differential cohomology in a cohesive infinity-topos Authors: Urs Schreiber Categories: math-ph hep-th math.AT math.DG math.MP Comments: 797 pages \\ We formulate differential cohomology and Chern-Weil theory -- the theory of connections on fiber bundles and of gauge fields -- abstractly in the context of a certain class of higher toposes that we call "cohesive". Cocycles in this differential cohomology classify higher principal bundles equipped with cohesive structure (topological, smooth, synthetic differential, supergeometric, etc.) and equipped with connections, hence higher gauge fields. We discuss various models of the axioms and applications to fundamental notions and constructions in quantum field theory and string theory. In particular we show that the cohesive and differential refinement of universal characteristic cocycles constitutes a higher Chern-Weil homomorphism refined from secondary caracteristic classes to morphisms of higher moduli stacks of higher gauge fields, and at the same time constitutes extended geometric prequantization -- in the sense of extended/multi-tiered quantum field theory -- of hierarchies of higher dimensional Chern-Simons-type field theories, their higher Wess-Zumino-Witten-type boundary field theories and all further higher codimension defect field theories. We close with an outlook on the cohomological quantization of such higher boundary prequantum field theories by a kind of cohesive motives. \\ ( http://arxiv.org/abs/1310.7930 , 788kb) %-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%- ------------------------------------------------------------------------------ \\ arXiv:1310.5606 (*cross-listing*) Date: Mon, 21 Oct 2013 15:36:25 GMT (1400kb) Title: Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space Authors: Roland Donninger and Joachim Krieger and Jeremie Szeftel and Willie Wong Categories: math.AP math-ph math.DG math.MP Comments: 59 pages, 2 figures MSC-class: 35L72, 35B40, 35B30, 35B44, 53A10 \\ We study time-like hypersurfaces with vanishing mean curvature in the (3+1) dimensional Minkowski space, which are the hyperbolic counterparts to minimal embeddings of Riemannian manifolds. The catenoid is a stationary solution of the associated Cauchy problem. This solution is linearly unstable, and we show that this instability is the only obstruction to the global nonlinear stability of the catenoid. More precisely, we prove in a certain symmetry class the existence, in the neighborhood of the catenoid initial data, of a co-dimension 1 Lipschitz manifold transverse to the unstable mode consisting of initial data whose solutions exist globally in time and converge asymptotically to the catenoid. \\ ( http://arxiv.org/abs/1310.5606 , 1400kb) ------------------------------------------------------------------------------ \\ arXiv:1310.7570 (*cross-listing*) Date: Mon, 28 Oct 2013 13:05:19 GMT (15kb) Title: Finite dimensional representations of the elliptic modular double Authors: S. E. Derkachov, V. P. Spiridonov Categories: math.QA math-ph math.MP Comments: 13 pp \\ We describe a set of zero modes of an integral operator depending on one parameter $g$ and defining an elliptic Fourier transformation. This operator intertwines generators of the elliptic modular double formed from a pair of Sklyanin algebras. It has zero modes for the "spin" lattices $g=n\eta + m\tau/2$ and $g=1/2+n\eta + m\tau/2$ with incommensurate $1, 2\eta,\tau$, and Im$(\tau)$, Im$(\eta)>0$, $n,m\in\mathbb{Z}_{\geq 0},(n,m)\neq (0,0)$. These modes define finite dimensional representations of the elliptic modular double of dimension $d=nm$ for $n,m\in\mathbb{Z}_{>0}$ or $d=n\in \mathbb{Z}_{>0}$ for $m=0$ and $d=m\in \mathbb{Z}_{>0}$ for $n=0$. \\ ( http://arxiv.org/abs/1310.7570 , 15kb) ------------------------------------------------------------------------------ \\ arXiv:1310.7649 (*cross-listing*) Date: Mon, 28 Oct 2013 23:50:52 GMT (155kb) Title: The solution to the BCS gap equation for superconductivity and its temperature dependence Authors: Shuji Watanabe Categories: math.FA cond-mat.supr-con math-ph math.MP Comments: In this paper we can set $\varepsilon=0$ MSC-class: 47G10, 47H10, 47N50, 82D55 Journal-ref: Abstract and Applied Analysis, Volume 2013, Article ID 932085, 2013 DOI: 10.1155/2013/932085 \\ From the viewpoint of operator theory, we deal with the temperature dependence of the solution to the BCS gap equation for superconductivity. When the potential is a positive constant, the BCS gap equation reduces to the simple gap equation. We first show that there is a unique nonnegative solution to the simple gap equation, that it is continuous and strictly decreasing, and that it is of class $C^2$ with respect to the temperature. We next deal with the case where the potential is not a constant but a function. When the potential is not a constant, we give another proof of the existence and uniqueness of the solution to the BCS gap equation, and show how the solution varies with the temperature. We finally show that the solution to the BCS gap equation is indeed continuous with respect to both the temperature and the energy under a certain condition when the potential is not a constant. \\ ( http://arxiv.org/abs/1310.7649 , 155kb) ------------------------------------------------------------------------------ \\ arXiv:1310.7676 (*cross-listing*) Date: Tue, 29 Oct 2013 03:48:02 GMT (8kb) Title: Transformation formulas for bilinear sums of basic hypergeometric series Authors: Yasushi Kajihara Categories: math.CA math-ph math.MP math.QA math.RT Comments: 7 pages \\ A master formula of transformation formulas for bilinear sums of basic hypergeometric series is proposed. It is obtained from the author's previous results on a transformation formula for Milne's multivariate generalization of basic hypergeometric series of type $A$ with different dimensions and it can be considered as a generalization of Whipple-Sears transformation formula for terminating balanced ${}_4 \phi_3$ series. As an application of the master formula, one variable cases of some transformation formulas for bilinear sums of basic hypergeometric series are given as examples. The bilinear transformation formulas seem to be new in the literature even in one variable case. \\ ( http://arxiv.org/abs/1310.7676 , 8kb) ------------------------------------------------------------------------------ \\ arXiv:1310.7710 (*cross-listing*) Date: Tue, 29 Oct 2013 08:48:35 GMT (27kb,D) Title: Non-Abelian Self-Dual Strings in Six Dimensions from Four Dimensional 1/2-BPS Monopoles Authors: Chong-Sun Chu Categories: hep-th math-ph math.MP Comments: 18 pages, 2 figures, LaTeX \\ We find a new general construction of self-dual string solutions to the non-abelian two-form self-duality equation proposed in \cite{CK}. This class of self-dual strings is determined by the BPS monopoles in four-dimensions. Our construction covers the self-dual string solutions found previously. As a new example, we construct a new self-dual string solution that is based on the BPS 't Hooft-Polyakov monopole. As BPS monopoles are generally given by the Nahm construction, our construction suggests that a generalized Nahm transform may exist for the non-abelian self-dual strings. \\ ( http://arxiv.org/abs/1310.7710 , 27kb) ------------------------------------------------------------------------------ \\ arXiv:1310.7775 (*cross-listing*) Date: Tue, 29 Oct 2013 12:04:28 GMT (23kb) Title: The glassy phase of complex branching Brownian motion Authors: Thomas Madaule (UP13), R\'emi Rhodes (CEREMADE), Vincent Vargas (DMA) Categories: math.PR math-ph math.MP Comments: 23 pages \\ In this paper, we study complex valued branching Brownian motion in the so-called glassy phase, or also called phase II. In this context, we prove a limit theorem for the complex partition function hence confirming a conjecture formulated by the last two authors in a previous paper on complex Gaussian multiplicative chaos. We will show that the limiting partition function can be expressed as a product of a Gaussian random variable, mainly due to the windings of the phase, and a stable transform of the so called derivative martingale, mainly due to the clustering of the modulus. The proof relies on the fine description of the extremal process available in the branching Brownian motion context. \\ ( http://arxiv.org/abs/1310.7775 , 23kb) ------------------------------------------------------------------------------ \\ arXiv:1310.7885 (*cross-listing*) Date: Tue, 29 Oct 2013 17:16:05 GMT (9kb) Title: Quantum Indeterminacy, Polar Duality, and Symplectic Capacities Authors: Maurice A. de Gosson Categories: quant-ph math-ph math.MP Comments: Submitted \\ The notion of polarity between sets, well-known from convex geometry, is a geometric version of the Fourier transform. We exploit this analogy to propose a new simple definition of quantum indeterminacy, using what we call "hbar-polar quantum pairs", which can be viewed as pairs of position-momentum indeterminacy with minimum spread. The existence of such pairs is guaranteed by the usual uncertainty principle, but is at the same time more general. We use recent advances in symplectic topology to show that this quantum indeterminacy can be measured using a particular symplectic capacity related to action and which reduces to area in the case of one degree of freedom. We show in addition that polar quantum pairs are closely related to Hardy's uncertainty principle about the localization of a function and its Fourier transform. \\ ( http://arxiv.org/abs/1310.7885 , 9kb) %%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%% ------------------------------------------------------------------------------ \\ arXiv:1210.1571 replaced with revised version Tue, 29 Oct 2013 09:32:14 GMT (14kb,D) Title: The singular kernel coagulation equation with multifragmentation Authors: Carlos Cueto Camejo, Gerald Warnecke Categories: math-ph math.MP Comments: 16 pages. arXiv admin note: substantial text overlap with arXiv:1210.1500 \\ ( http://arxiv.org/abs/1210.1571 , 14kb) ------------------------------------------------------------------------------ \\ arXiv:1304.1409 replaced with revised version Tue, 29 Oct 2013 01:34:47 GMT (143kb) Title: Fragmentation dynamics of DNA sequence duplications Authors: M.V. Koroteev, J. Miller Categories: math-ph math.MP q-bio.PE Comments: 5 pages, 4 figures \\ ( http://arxiv.org/abs/1304.1409 , 143kb) ------------------------------------------------------------------------------ \\ arXiv:1304.7569 (*cross-listing*) replaced with revised version Tue, 29 Oct 2013 06:53:46 GMT (41kb,D) Title: First order global asymptotics for confined particles with singular pair repulsion Authors: Djalil Chafa\"i (CEREMADE, LAMA), Nathael Gozlan (LAMA), Pierre-Andr\'e Zitt (LAMA) Categories: math.PR math-ph math.CA math.MP Comments: New title. Added references. Minor core revision \\ ( http://arxiv.org/abs/1304.7569 , 41kb) ------------------------------------------------------------------------------ \\ arXiv:1304.8079 (*cross-listing*) replaced with revised version Tue, 29 Oct 2013 17:15:37 GMT (79kb,D) Title: Non-perturbative black holes in Type-IIA String Theory vs. the No-Hair conjecture Authors: Pablo Bueno and C. S. Shahbazi Categories: hep-th gr-qc math-ph math.MP Comments: 7 pages, 1 figure. Final version. To appear in CQG Report-no: IFT-UAM/CSIC-13-054 \\ ( http://arxiv.org/abs/1304.8079 , 79kb) ------------------------------------------------------------------------------ \\ arXiv:1305.3641 replaced with revised version Mon, 28 Oct 2013 20:31:09 GMT (375kb,D) Title: Excitation spectrum of interacting bosons in the mean-field infinite-volume limit Authors: Jan Derezi\'nski and Marcin Napi\'orkowski Categories: math-ph cond-mat.quant-gas cond-mat.stat-mech math.MP Comments: Revised and extended version. 26 pages, 4 figures. To appear in Annales Henri Poincar\'e \\ ( http://arxiv.org/abs/1305.3641 , 375kb) ------------------------------------------------------------------------------ \\ arXiv:1309.0816 (*cross-listing*) replaced with revised version Tue, 29 Oct 2013 10:47:58 GMT (95kb,D) Title: Locality of temperature Authors: M. Kliesch, C. Gogolin, M. J. Kastoryano, A. Riera, J. Eisert Categories: quant-ph cond-mat.stat-mech math-ph math.MP Comments: 5 pages + 6 pages appendix, 2 figures, improved presentation \\ ( http://arxiv.org/abs/1309.0816 , 95kb) ------------------------------------------------------------------------------ \\ arXiv:1310.2799 (*cross-listing*) replaced with revised version Tue, 29 Oct 2013 13:37:13 GMT (4kb) Title: Free Particle Wave Function and Niederer's Transformation Authors: K. Andrzejewski, J. Gonera, P. Kosinski Categories: quant-ph math-ph math.MP \\ ( http://arxiv.org/abs/1310.2799 , 4kb) ------------------------------------------------------------------------------ \\ arXiv:1310.6510 (*cross-listing*) replaced with revised version Tue, 29 Oct 2013 01:15:15 GMT (284kb) Title: On topological instabilities arising in families of semilinear parabolic problems Authors: Mickael D. Chekroun Categories: math.AP math-ph math.DS math.MP Comments: 1 figure, 23 pages MSC-class: 35J61, 35B30, 35B32, 35B20, 35K58, 35A16, 37K50, 37C20, 37H20, 37J20, 47H11 \\ ( http://arxiv.org/abs/1310.6510 , 284kb) ------------------------------------------------------------------------------ \\ arXiv:1310.7395 (*cross-listing*) replaced with revised version Tue, 29 Oct 2013 01:44:47 GMT (100kb,D) Title: Instability of enclosed horizons Authors: Bernard S. Kay (York) Categories: gr-qc hep-th math-ph math.MP Comments: 9 pages, 3 figures (small but important correction to the wording in three lines -- including a line of the abstract) \\ ( http://arxiv.org/abs/1310.7395 , 100kb) %%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%--- For subscribe options to combined physics archives, e-mail To: physics@arXiv.org, Subject: subscribe ----------------------------------------------------------------------------- For help on viewing and making submissions, see http://arXiv.org/help/ For a list of archive mirror sites, see http://arXiv.org/servers.html ----------------------------------------------------------------------------- Third-party submissions cause excessive problems. Author self-submissions are exceedingly preferred. E-mail submissions have been discontinued in favor of better support for Web submissions. See http://arXiv.org/help/uploads