Date: Fri, 29 Apr 11 00:05:25 GMT Subject: math-ph daily 7 new + 9 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 Wed 27 Apr 11 20:00:00 GMT to Thu 28 Apr 11 20:00:00 GMT ------------------------------------------------------------------------------ \\ arXiv:1104.5251 Date: Wed, 27 Apr 2011 21:27:21 GMT (24kb,D) Title: Quantum Fields bounded by one dimensional crystal plates Authors: J.M. Munoz-Castaneda, M. Bordag Categories: math-ph hep-th math.MP Comments: 18 pages, 1 figure \\ We get deeper understanding of the role played by boundary conditions in quantum field theory, by studying the structure of a scalar massless quantum field theory bounded by two one dimensional planar crystal plates. The system can also be understood as a massless scalar confined to propagate in the surface of a finite cylinder. We classify the most general type of regular behaved boundary conditions that the quantum field can satisfy, in accordance with the unitarity principle of quantum field theory. Also, we characterize the frequency spectrum for each quantum field theory, by computing the holomorphic spectral function. The spectral function is the starting point to compute the Casimir energy as a global function over the space of allowed boundary conditions for the quantum field theory. \\ ( http://arxiv.org/abs/1104.5251 , 24kb) ------------------------------------------------------------------------------ \\ arXiv:1104.5264 Date: Wed, 27 Apr 2011 22:46:12 GMT (16kb) Title: On the many Dirichlet Laplacians on a non-convex polygon and their approximations by point interactions Authors: Andrea Posilicano Categories: math-ph math.MP \\ By Birman and Skvortsov it is known that if $\Omega$ is a plane curvilinear polygon with $n$ non-convex corners then the Laplace operator with domain $H^2(\Omega)\cap H^1_0(\Omega)$ is a closed symmetric operator with deficiency indices $(n,n)$. Here, by providing all self-adjoint extensions of such a symmetric operator, we determine the set of self-adjoint non-Friedrichs Dirichlet Laplacians on $\Omega$ and, by a corresponding Krein-type resolvent formula, show that any element in this set is the norm resolvent limit of a suitable sequence of Friedrichs-Dirichlet Laplacians with $n$ point interactions. \\ ( http://arxiv.org/abs/1104.5264 , 16kb) ------------------------------------------------------------------------------ \\ arXiv:1104.5273 Date: Wed, 27 Apr 2011 23:50:03 GMT (13kb) Title: Phase coherent states with circular Jacobi polynomials for the pseudoharmonic oscillator Authors: Zouhair Mouayn Categories: math-ph math.MP Comments: 16 pages \\ We construct a class of generalized phase coherent states indexed by points of the unit circle and depending on three positive parameters "gamma","alpha" and "epsilon" by replacing the labelling coefficients of the canonical coherent states by circular Jacobi polynomials with parameter "gamma". The special case "gamma" = 0 corresponds to well known phase coherent phase states. The constructed states are superposition of eigenstates of a one-parameter pseudoharmonic oscillator depending on "alpha" and solve the identity of the state Hilbert space at the limit "epsilon"->0+. Closed form for their wavefunctions are obtained in the case "alpha" = "gamma" + 1 and their associated coherent states transform is defined. \\ ( http://arxiv.org/abs/1104.5273 , 13kb) ------------------------------------------------------------------------------ \\ arXiv:1104.5274 Date: Thu, 28 Apr 2011 00:02:39 GMT (27kb) Title: KAM theory for quasi-periodic equilibria in 1-D quasiperiodic media Authors: Xifeng Su and Rafael de la Llave Categories: math-ph math.DS math.MP MSC-class: 70K43, 52C23, 37A60, 37J40, 82B20 \\ We consider Frenkel-Kontorova models corresponding to 1 dimensional quasicrystals. We present a KAM theory for quasi-periodic equilibria. The theorem presented has an \emph{a-posteriori} format. We show that, given an approximate solution of the equilibrium equation, which satisfies some appropriate non-degeneracy conditions, then, there is a true solution nearby. This solution is locally unique. Such a-posteriori theorems can be used to validate numerical computations and also lead immediately to several consequences a) Existence to all orders of perturbative expansion and their convergence b) Bootstrap for regularity c) An efficient method to compute the breakdown of analyticity. Since the system does not admit an easy dynamical formulation, the method of proof is based on developing several identities. These identities also lead to very efficient algorithms. \\ ( http://arxiv.org/abs/1104.5274 , 27kb) ------------------------------------------------------------------------------ \\ arXiv:1104.5315 Date: Thu, 28 Apr 2011 07:42:24 GMT (77kb) Title: Asymptotic Analysis of the Wigner $3j$-Symbol in the Bargmann Representation Authors: Liang Yu Categories: math-ph math.MP Comments: 23 pages, 2 figures \\ We derive the leading asymptotic limit of the Wigner $3j$-symbol from a stationary phase approximation of a twelve dimensional integral, obtained from an inner product between two exact Bargmann wavefunctions. We show that, by the construction of the Bargmann inner product, the stationary phase conditions have a geometric description in terms of the Hopf fibration of ${\mathbb C}^6$ into ${\mathbb R}^3 \times {\mathbb R}^3 \times {\mathbb R}^3$. In addition, we find that, except for the usual modification of the quantum numbers by 1/2, the imaginary part of the logarithm of a Bargmann wavefunction, evaluated at the stationary points, is equal to the asymptotic phase of the $3j$-symbol. \\ ( http://arxiv.org/abs/1104.5315 , 77kb) ------------------------------------------------------------------------------ \\ arXiv:1104.5423 Date: Thu, 28 Apr 2011 15:23:08 GMT (199kb) Title: Influence of rotation speed on natural frequency: A short introduction and presentation of an imaginary 'antigravity' world Authors: Christopher G. Provatidis Categories: math-ph math.MP Comments: 7 pages, 3 figures \\ We present an instructive way to introduce the subject of resonance using a typical spring-mass system without damping. In contrast to the standard approach found in most textbooks, here we propose a way to extend the lectures from common translational systems to rotating ones. In the latter case, particular attention is paid to the role of the variable centripetal force. The students will find analytical solutions of the simplest possible ordinary differential equations of motion and see that the natural frequency strongly depends on the rotation speed, the latter being a simple vector sum. The analysis reveals that always the resultant ground force is harmonic. In order to depict the significance in the influence of rotation on natural frequency, we present an imaginary 'antigravity' world in which the aforementioned dependency is absent. \\ ( http://arxiv.org/abs/1104.5423 , 199kb) ------------------------------------------------------------------------------ \\ arXiv:1104.5482 Date: Thu, 28 Apr 2011 19:36:59 GMT (24kb) Title: Universal Probability Distribution for the Wave Function of an Open Quantum System Authors: Sheldon Goldstein, Joel L. Lebowitz, Christian Mastrodonato, Roderich Tumulka, Nino Zanghi Categories: math-ph math.MP quant-ph Comments: 28 pages LaTeX, no figures \\ An open quantum system (i.e., one that interacts with its environment) is almost always entangled with its environment; it is therefore usually not attributed a wave function but only a reduced density matrix rho. Nevertheless, there is a precise way of attributing to it a wave function psi_1, called its conditional wave function, which is a random wave function of the system whose probability distribution mu_1 depends on the entangled wave function psi in the Hilbert space of system and environment together. We prove several universality (or typicality) results about mu_1; they show that if the environment is sufficiently large then mu_1 does not depend much on the details of psi and is approximately given by one of the so-called GAP measures. Specifically, for most entangled states psi with given reduced density matrix rho_1, mu_1 is close to GAP(rho_1). We also show that, if the coupling between the system and the environment is weak, then for most entangled states psi from a microcanonical subspace corresponding to energies in a narrow interval [E,E+delta E] (and most bases of Hilbert space 2), mu_1 is close to GAP(rho_beta) with rho_beta the canonical density matrix on Hilbert space 1 at inverse temperature beta=beta(E). This provides the mathematical justification of the claim that GAP(rho_beta) is the thermal equilibrium distribution of psi_1. \\ ( http://arxiv.org/abs/1104.5482 , 24kb) %-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%- ------------------------------------------------------------------------------ \\ arXiv:1104.5231 (*cross-listing*) Date: Wed, 27 Apr 2011 20:00:02 GMT (71kb) Title: Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons Authors: Alexander S. Haupt, Tatiana A. Ivanova, Olaf Lechtenfeld, Alexander D. Popov Categories: hep-th math-ph math.MP Comments: 1+17 pages, 1 figure \\ Due to their explicit construction, Aloff-Wallach spaces are prominent in flux compactifications. They carry G_2-structures and admit the G_2-instanton equations, which are natural BPS equations for Yang-Mills instantons on seven-manifolds and extremize a Chern-Simons-type functional. We consider the Chern-Simons flow between different G_2-instantons on Aloff-Wallach spaces, which is equivalent to Spin(7)-instantons on a cylinder over them. For a general SU(3)-equivariant gauge connection, the generalized instanton equations turn into gradient-flow equations on C^3 x R^2, with a particular cubic superpotential. For the simplest member of the Aloff-Wallach family (with 3-Sasakian structure) we present an explicit instanton solution of tanh-like shape. \\ ( http://arxiv.org/abs/1104.5231 , 71kb) ------------------------------------------------------------------------------ \\ arXiv:1104.5242 (*cross-listing*) Date: Wed, 27 Apr 2011 20:28:13 GMT (92kb) Title: Introduction to the Time Evolution of Open Quantum Systems Authors: \'Angel Rivas and Susana F. Huelga Categories: quant-ph cond-mat.quant-gas cond-mat.stat-mech math-ph math.MP physics.atom-ph physics.chem-ph Comments: 101 pages, 3 figures. Comments and suggestions are most welcome \\ We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and methods traditionally employed by different communities. We present in some detail the mathematical structure and the general properties of the dynamical maps underlying open system dynamics. We also discuss the microscopic derivation of dynamical equations, including both Markovian and non-Markovian evolutions. \\ ( http://arxiv.org/abs/1104.5242 , 92kb) ------------------------------------------------------------------------------ \\ arXiv:1104.5277 (*cross-listing*) Date: Thu, 28 Apr 2011 02:03:47 GMT (25kb) Title: Instability of Nonsymmetric Nonmonotone Equilibria of the Vlasov-Maxwell System Authors: Jonathan Ben-Artzi Categories: math.AP math-ph math.MP math.SP Comments: 19 pages \\ We consider the 1/2-dimensional relativistic Vlasov-Maxwell system that describes the time-evolution of a plasma. We find a relatively simple criterion for spectral instability of a wide class of equilibria. This class includes non-homogeneous equilibria that need not satisfy any additional symmetry properties (as was the case in previous results), nor should they be monotone in the particle energy. The criterion is given in terms of the spectral properties of two Schr\"{o}dinger operators that arise naturally from Maxwell's equations. The spectral analysis of these operators is quite delicate, and some general functional analytic tools are developed to treat them. These tools can be applied to similar systems in higher dimensions, as long as their domain is finite or periodic. \\ ( http://arxiv.org/abs/1104.5277 , 25kb) ------------------------------------------------------------------------------ \\ arXiv:1104.5293 (*cross-listing*) Date: Thu, 28 Apr 2011 04:14:46 GMT (659kb,D) Title: Fast multi-particle scattering: a hybrid solver for the Maxwell equations in microstructured materials Authors: Zydrunas Gimbutas and Leslie Greengard Categories: math.NA math-ph math.MP Comments: 19 pages, 4 figures \\ A variety of problems in device and materials design require the rapid forward modeling of Maxwell's equations in complex micro-structured materials. By combining high-order accurate integral equation methods with classical multiple scattering theory, we have created an effective simulation tool for materials consisting of an isotropic background in which are dispersed a large number of micro- or nano-scale metallic or dielectric inclusions. \\ ( http://arxiv.org/abs/1104.5293 , 659kb) ------------------------------------------------------------------------------ \\ arXiv:1104.5312 (*cross-listing*) Date: Thu, 28 Apr 2011 07:00:05 GMT (9kb) Title: Tensor models and hierarchy of n-ary algebras Authors: Naoki Sasakura Categories: hep-th gr-qc math-ph math.MP Comments: 13 pages Report-no: YITP-11-51 \\ Tensor models are generalization of matrix models, and are studied as models of quantum gravity. It is shown that the symmetry of the rank-three tensor models is generated by a hierarchy of n-ary algebras starting from the usual commutator, and the 3-ary algebra symmetry reported in the previous paper is just a single sector of the whole structure. The condition for the Leibnitz rules of the n-ary algebras is discussed from the perspective of the invariance of the underlying algebra under the n-ary transformations. It is shown that the n-ary transformations which keep the underlying algebraic structure invariant form closed finite n-ary Lie subalgebras. It is also shown that, in physical settings, the 3-ary transformation practically generates only local infinitesimal symmetry transformations, and the other more non-local infinitesimal symmetry transformations of the tensor models are generated by higher n-ary transformations. \\ ( http://arxiv.org/abs/1104.5312 , 9kb) ------------------------------------------------------------------------------ \\ arXiv:1104.5367 (*cross-listing*) Date: Thu, 28 Apr 2011 12:14:25 GMT (25kb) Title: Global estimates of fundamental solutions for higher-order Schr\"odinger equations Authors: JinMyong Kim Categories: math.AP math-ph math.MP MSC-class: (2000). 42B25, 42A45, 35Q53, 35Q35 \\ In this paper we first establish global pointwise time-space estimates of the fundamental solution for Schr\"odinger equations, where the symbol of the spatial operator is a real non-degenerate elliptic polynomial. Then we use such estimates to establish related Lp-Lq estimates on the Schr\"odinger solution. These estimates extend known results from the literature and are sharp. This result was latetly already generalized to a degenerate case (cf. [9]). \\ ( http://arxiv.org/abs/1104.5367 , 25kb) ------------------------------------------------------------------------------ \\ arXiv:1104.5438 (*cross-listing*) Date: Thu, 28 Apr 2011 16:27:06 GMT (34kb) Title: Bulk deformations of open topological string theory Authors: Nils Carqueville, Michael M. Kay Categories: hep-th math-ph math.MP math.QA Comments: 39 pages \\ We present a general method to construct bulk-deformed open topological string theories from Landau-Ginzburg models. To this end we obtain a weak version of deformation quantisation, and we show how this together with the technique of homological perturbation allows to explicitly compute all bulk-deformed open topological string amplitudes at tree-level before tadpole-cancellation. Our approach is based on a coherent treatment of the problem in terms of the fundamental A-infinity- and L-infinity-structures involved. \\ ( http://arxiv.org/abs/1104.5438 , 34kb) ------------------------------------------------------------------------------ \\ arXiv:1104.5481 (*cross-listing*) Date: Thu, 28 Apr 2011 19:34:49 GMT (192kb) Title: Path Integral on Star Graph Authors: Satoshi Ohya Categories: hep-th math-ph math.MP quant-ph Comments: 19 pages, 15 figures Report-no: IFUP-TH/2011-9 \\ In this paper we study path integral for a single spinless particle on a star graph with N edges, whose vertex is known to be described by U(N) family of boundary conditions. After carefully studying the free particle case, both at the critical and off-critical levels, we propose new path integral formulation that correctly captures all the scale-invariant subfamily of boundary conditions realized at fixed points of boundary renormalization group flow. Our proposal is based on the folding trick, which maps a scalar-valued wave function on star graph to an N-component vector-valued wave function on half-line. All the parameters of scale-invariant subfamily of boundary conditions are encoded into the momentum independent weight factors, which appear to be associated with the two distinct path classes on half-line that form the cyclic group Z_2. We show that, when bulk interactions are edge-independent, these weight factors are generally given by an N-dimensional unitary representation of Z_2. Generalization to momentum dependent weight factors and applications to worldline formalism are briefly discussed. \\ ( http://arxiv.org/abs/1104.5481 , 192kb) ------------------------------------------------------------------------------ \\ arXiv:1104.5489 (*cross-listing*) Date: Thu, 28 Apr 2011 19:56:04 GMT (21kb) Title: Extended trigonometric Cherednik algebras and nonstationary Schr\"odinger equations with delta-potentials Authors: Jonas T. Hartwig, Jasper V. Stokman Categories: math.RT math-ph math.MP Comments: 23 pages \\ We realize an extended version of the trigonometric Cherednik algebra as affine Dunkl operators involving Heaviside functions. We use the quadratic Casimir element of the extended trigonometric Cherednik algebra to define an explicit nonstationary Schr\"odinger equation with delta-potential. We use coordinate Bethe ansatz methods to construct solutions of the nonstationary Schr\"odinger equation in terms of generalized Bethe wave functions. It is shown that the generalized Bethe wave functions satisfy affine difference Knizhnik-Zamolodchikov equations in their spectral parameter. The relation to the vector valued root system analogs of the Lieb-Liniger model on the circle is indicated. \\ ( http://arxiv.org/abs/1104.5489 , 21kb) %%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%% ------------------------------------------------------------------------------ \\ arXiv:nlin/0206034 (*cross-listing*) replaced with revised version Wed, 27 Apr 2011 20:59:14 GMT (5kb) Title: Integrability of the Bakirov system: a zero-curvature representation Authors: Sergei Sakovich Categories: nlin.SI math-ph math.AP math.MP Comments: 6 pages Journal-ref: Int. J. Math. Math. Sci. 2011 (2011) 497828 (7 pages) DOI: 10.1155/2011/497828 \\ ( http://arxiv.org/abs/nlin/0206034 , 5kb) ------------------------------------------------------------------------------ \\ arXiv:0911.2102 (*cross-listing*) replaced with revised version Thu, 28 Apr 2011 07:10:55 GMT (24kb) Title: A Formulation of Quantum Field Theory Realizing a Sea of Interacting Dirac Particles Authors: Felix Finster Categories: hep-th math-ph math.MP Comments: 16 pages, LaTeX, 1 figure, minor changes (published version) Journal-ref: Lett. Math. Phys. 97 (2011) DOI: 10.1007/s11005-011-0473-1 \\ ( http://arxiv.org/abs/0911.2102 , 24kb) ------------------------------------------------------------------------------ \\ arXiv:1001.3556 replaced with revised version Thu, 28 Apr 2011 19:28:53 GMT (17kb) Title: A new proof of the Vorono\"i summation formula Authors: Sebastian Egger n\'e Endres and Frank Steiner Categories: math-ph math.MP Comments: Enlarged version of a accepted paper by J. Phys. A: Math. Theor \\ ( http://arxiv.org/abs/1001.3556 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:1008.2451 replaced with revised version Thu, 28 Apr 2011 00:09:52 GMT (39kb) Title: Instability of Nonmonotone Magnetic Equilibria of the Relativistic Vlasov-Maxwell System Authors: Jonathan Ben-Artzi Categories: math-ph math.AP math.MP Comments: 46 pages \\ ( http://arxiv.org/abs/1008.2451 , 39kb) ------------------------------------------------------------------------------ \\ arXiv:1102.2796 (*cross-listing*) replaced with revised version Thu, 28 Apr 2011 12:52:03 GMT (507kb) Title: On the Kolmogorov-Sinai entropy of many-body Hamiltonian systems Authors: Arul Lakshminarayan and Steven Tomsovic Categories: nlin.CD math-ph math.MP Comments: 5 figures, resubmitted to Phys. Rev. E \\ ( http://arxiv.org/abs/1102.2796 , 507kb) ------------------------------------------------------------------------------ \\ arXiv:1103.5617 replaced with revised version Thu, 28 Apr 2011 08:34:53 GMT (123kb,D) Title: Compact smallest eigenvalue expressions in Wishart-Laguerre ensembles with or without fixed-trace Authors: Gernot Akemann, Pierpaolo Vivo Categories: math-ph cond-mat.stat-mech hep-th math.MP Comments: 25 pag., 4 fig - minor changes, typos fixed. To appear in JSTAT \\ ( http://arxiv.org/abs/1103.5617 , 123kb) ------------------------------------------------------------------------------ \\ arXiv:1104.0785 (*cross-listing*) replaced with revised version Thu, 28 Apr 2011 15:40:36 GMT (37kb) Title: The mixed boundary value problem, Krein resolvent formulas and spectral asymptotic estimates Authors: Gerd Grubb Categories: math.AP math-ph math.MP math.SP Comments: 29 pages, proofreading corrections, to appear in J. Math. Anal. Appl MSC-class: 35J25, 35P20, 47G30, 58J40 \\ ( http://arxiv.org/abs/1104.0785 , 37kb) ------------------------------------------------------------------------------ \\ arXiv:1104.1059 (*cross-listing*) replaced with revised version Thu, 28 Apr 2011 19:16:51 GMT (207kb) Title: Time dependent transitions with time-space noncommutativity & its implications in Quantum Optics Authors: Nitin Chandra Categories: hep-th hep-ph math-ph math.MP quant-ph Comments: 15 pages, 4 figures \\ ( http://arxiv.org/abs/1104.1059 , 207kb) %%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%--- 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