Journal of Mathematical Physics: All Topics

The coincidence limit of the graviton propagator in de Donder gauge on de Sitter background

E. O. Kahya, S. P. Miao, and R. P. Woodard
We explicitly work out the de Sitter breaking contributions to the recent solution for the de Donder gauge graviton propagator on de Sitter. We also provide explicit power series expansions for the two structure functions, which are suitable for implementing dimensional regularization. And we evalua ... [J. Math. Phys. 53, 022304 (2012)] published Fri Feb 10, 2012.

Noncommutative deformation of spinor zero mode and Atiyah-Drinfeld-Hitchin-Manin construction

Yoshiaki Maeda and Akifumi Sako
A method to construct noncommutative instantons as deformations from commutative instantons was provided by Maeda and Sako [J. Geom. Phys. 58, 1784 (2008)]. Using this noncommutative deformed instanton, we investigate the spinor zero modes of the Dirac operator in a noncommutative instanton backgrou ... [J. Math. Phys. 53, 022303 (2012)] published Fri Feb 10, 2012.

Classical group field theory

Joseph Ben Geloun
The ordinary formalism for classical field theory is applied to dynamical group field theories. Focusing first on a local group field theory over one copy of SU(2) and then, on more involved nonlocal theories (colored and noncolored) defined over a tensor product of the same group, we address the is ... [J. Math. Phys. 53, 022901 (2012)] published Thu Feb 9, 2012.

On flavor symmetry in lattice quantum chromodynamics

El Hassan Saidi
Using a well established method to engineer non-abelian symmetries in superstring compactifications, we study the link between the point splitting method of Creutz et al. [PoS: Lattice 2010, 078 (2010) and JHEP 041, 1012 (2010)] for implementing flavor symmetry in lattice QCD; and singularity theo ... [J. Math. Phys. 53, 022302 (2012)] published Thu Feb 9, 2012.

Discretising the Painleve equations a la Hirota-Mickens

B. Grammaticos, A. Ramani, J. Satsuma, and R. Willox
We present a systematic method for discretising the Painleve equations inspired by the method of Hirota (while extending it) and by that of Mickens (by specifying it to the case at hand). We derive various discrete analogues of Painleve I and II. We obtain forms that have been previously derived as ... [J. Math. Phys. 53, 023506 (2012)] published Thu Feb 9, 2012.

The two-dimensional Euler-Poisson system with spherical symmetry

Juhi Jang
This article concerns the global-in-time existence of smooth solutions with small amplitude to two space dimensional Euler-Poisson system. The main difficulty lies in the slow time decay (1 + t) of the linear system. Inspired by the work of Ozawa et al., [Global existence and asymptotic behavior of ... [J. Math. Phys. 53, 023701 (2012)] published Wed Feb 8, 2012.

A note on the first integrals of the ABC system

Jaume Llibre and Claudia Valls
Without loss of generality the ABC systems reduce to two cases: either A = 0 and B, C >= 0, or A = 1 and 0 < B, C <= 1. In the first case it is known that the ABC system is completely integrable, here we provide its explicit first integrals. In the second case Ziglin [Dichotomy of the separatrices a ... [J. Math. Phys. 53, 023505 (2012)] published Wed Feb 8, 2012.

Rational solutions of the Noumi and Yamada system of type A

Kazuhide Matsuda
We completely classify the rational solutions of the Noumi and Yamada system of type A, which is a generalization of the fourth Painleve equation. The rational solutions are classified to three by the Backlund transformation group. ... [J. Math. Phys. 53, 023504 (2012)] published Wed Feb 8, 2012.

Asymptotic stability of vacuum twisting type II metrics

Wlodzimierz Natorf
We generalize the result of Lukacs et al. on asymptotic stability of the Schwarzschild metric with respect to perturbations in the Robinson-Trautman class of metrics to the case of Petrov type II twisting metrics, under the condition of asymptotic flatness at future null infinity. The Bondi energy i ... [J. Math. Phys. 53, 022503 (2012)] published Tue Feb 7, 2012.

On the variational homotopy perturbation method for nonlinear oscillators

Francisco M. Fernandez
In this paper, I discuss a recent application of a variational homotopy perturbation method to rather simple nonlinear oscillators. It is shown that the main equations are inconsistent and for that reason the results may be of scarce utility. ... [J. Math. Phys. 53, 024101 (2012)] published Tue Feb 7, 2012.

Planar waveguide with twisted boundary conditions: Small width

Denis Borisov and Giuseppe Cardone
We consider a planar waveguide with twisted boundary conditions. By twisting we mean a special combination of Dirichlet and Neumann boundary conditions. Assuming that the width of the waveguide goes to zero, we identify the effective (limiting) operator as the width of the waveguide tends to zero, e ... [J. Math. Phys. 53, 023503 (2012)] published Tue Feb 7, 2012.

Solitonic solutions of Faddeev model

Chang-Guang Shi and Minoru Hirayama
An application of the equation proposed by the present authors, which is equivalent to the static field equation of the Faddeev model, is discussed. Under some assumptions on the space and on the form of the solution, the field equation is reduced to a nonlinear ordinary differential equation of sec ... [J. Math. Phys. 53, 022301 (2012)] published Tue Feb 7, 2012.

Spacelike hypersurfaces with negative total energy in de Sitter spacetime

Zhuobin Liang and Xiao Zhang
De Sitter spacetime can be separated into two parts along two kinds of hypersurfaces and the half-de Sitter spacetimes are covered by the planar and hyperbolic coordinates, respectively. Two positive energy theorems were proved previously for certain [script P]-asymptotically de Sitter and [script H ... [J. Math. Phys. 53, 022502 (2012)] published Fri Feb 3, 2012.

The holonomy group at infinity of the Painleve VI equation

Bassem Ben Hamed, Lubomir Gavrilov, and Martine Klughertz
We prove that the holonomy group at infinity of the Painleve VI equation is virtually commutative. ... [J. Math. Phys. 53, 022701 (2012)] published Fri Feb 3, 2012.

Convergence of expansions in Schrodinger and Dirac eigenfunctions, with an application to the R-matrix theory

Julia Stasinska
Expansion of a wave function in a basis of eigenfunctions of a differential eigenvalue problem lies at the heart of the R-matrix methods for both the Schrodinger and Dirac particles. A central issue that should be carefully analyzed when functional series are applied is their convergence. In the pre ... [J. Math. Phys. 53, 022101 (2012)] published Thu Feb 2, 2012.

Quantum deformation of two four-dimensional spin foam models

Winston J. Fairbairn and Catherine Meusburger
We construct the q-deformed version of two four-dimensional spin foam models, the Euclidean and Lorentzian versions of the Engle, Pereira, Rovelli and Livine (EPRL) model. The q-deformed models are based on the representation theory of two copies of U([fraktur su](2)) at a root of unity and on the q ... [J. Math. Phys. 53, 022501 (2012)] published Thu Feb 2, 2012.

Quasi-periodic functions on the torus and sl(n)-elliptic Lie algebra

T. Skrypnyk
We investigate properties of the sl(n) automorphic elliptic algebra [fraktur E](sl(n)). We prove it to be [openface Z] quasi-graded Lie algebra which could be viewed as a deformation of a graded loop algebra. We show that it admits the decomposition into the direct sum of two subalgebras: [fraktur E ... [J. Math. Phys. 53, 023502 (2012)] published Wed Feb 1, 2012.

Proof of rounding by quenched disorder of first order transitions in low-dimensional quantum systems

Michael Aizenman, Rafael L. Greenblatt, and Joel L. Lebowitz
We prove that for quantum lattice systems in d <= 2 dimensions the addition of quenched disorder rounds any first order phase transition in the corresponding conjugate order parameter, both at positive temperatures and at T = 0. For systems with continuous symmetry the statement extends up to d <= 4 ... [J. Math. Phys. 53, 023301 (2012)] published Wed Feb 1, 2012.

Inversion of a general hyperelliptic integral and particle motion in HoravaLifshitz black hole space-times

Victor Enolski, Betti Hartmann, Valeria Kagramanova, Jutta Kunz, Claus Lammerzahl et al.
The description of many dynamical problems such as the particle motion in higher dimensional spherically and axially symmetric space-times is reduced to the inversion of hyperelliptic integrals of all three kinds. The result of the inversion is defined locally, using the algebro-geometric techniques ... [J. Math. Phys. 53, 012504 (2012)] published Tue Jan 31, 2012.

[script PT] symmetric, Hermitian and [script P]-self-adjoint operators related to potentials in [script PT] quantum mechanics

Tomas Ya. Azizov and Carsten Trunk
In the recent years, a generalization H = p + x(ix) of the harmonic oscillator using a complex deformation was investigated, where epsilon is a real parameter. Here, we will consider the most simple case: epsilon even and x real. We will give a complete characterization of three different classes of ... [J. Math. Phys. 53, 012109 (2012)] published Tue Jan 31, 2012.

Block type symmetry of bigraded Toda hierarchy

Chuanzhong Li, Jingsong He, and Yucai Su
In this paper, we define Orlov-Schulman's operators M, M, and then use them to construct the additional symmetries of the bigraded Toda hierarchy. We further show that these additional symmetries form an interesting infinite-dimensional Lie algebra known as a Block type Lie algebra, whose structure ... [J. Math. Phys. 53, 013517 (2012)] published Mon Jan 30, 2012.

The trace formula for a point scatterer on a compact hyperbolic surface

Henrik Ueberschar
An exact trace formula for the perturbation of the Laplacian by a Dirac delta potential on a compact hyperbolic Riemann surface is derived. The formula can be considered an analogue of the Selberg trace formula. The difference of perturbed and unperturbed trace is expressed as an identity term plus ... [J. Math. Phys. 53, 012108 (2012)] published Mon Jan 30, 2012.

Coherences of accelerated detectors and the local character of the Unruh effect

Charis Anastopoulos and Ntina Savvidou
We study the locality of the acceleration temperature in the Unruh effect. To this end, we develop a new formalism for the modeling of macroscopic irreversible detectors. In particular, the formalism allows for the derivation of the higher-order coherence functions, analogous to the ones employed in ... [J. Math. Phys. 53, 012107 (2012)] published Mon Jan 30, 2012.

Affine reflection groups for tiling applications: Knot theory and DNA

M. Bodner, J. Patera, and M. Peterson
We present in this paper some non-conventional applications of affine Weyl groups W of rank 2, the symmetry group of the tiling/lattice. We first develop and present the tools for applications requiring tilings of a real Euclidean plane [openface R]. We then elucidate the equivalence of these tiling ... [J. Math. Phys. 53, 013516 (2012)] published Thu Jan 26, 2012.

Cohomology of line bundles: Applications

Ralph Blumenhagen, Benjamin Jurke, Thorsten Rahn, and Helmut Roschy
Massless modes of both heterotic and Type II string compactifications on compact manifolds are determined by vector bundle valued cohomology classes. Various applications of our recent algorithm for the computation of line bundle valued cohomology classes over toric varieties are presented. For the ... [J. Math. Phys. 53, 012302 (2012)] published Thu Jan 26, 2012.

Free field realization of quantum affine superalgebra U(sl-hat(N|1))

Takeo Kojima
We construct a free field realization of the quantum affine superalgebra U(sl-hat(N|1)) for an arbitrary level k[is-an-element-of][openface C]. ... [J. Math. Phys. 53, 013515 (2012)] published Wed Jan 25, 2012.

Generalized channels: Channels for convex subsets of the state space

Anna JenCova
Let K be a convex subset of the state space of a finite-dimensional C*-algebra. We study the properties of channels on K, which are defined as affine maps from K into the state space of another algebra, extending to completely positive maps on the subspace generated by K. We show that each such map ... [J. Math. Phys. 53, 012201 (2012)] published Wed Jan 25, 2012.

Dispersive estimates for harmonic oscillator systems

Vita Borovyk and Robert Sims
We consider a large class of harmonic systems, each defined as a quasi-free dynamics on the Weyl algebra over [script-l]([openface Z]). In contrast to recently obtained, short-time locality estimates, known as Lieb-Robinson bounds, we prove a number of long-time dispersive estimates for these models ... [J. Math. Phys. 53, 013302 (2012)] published Mon Jan 23, 2012.

Fractional Brownian sheets run with nonlinear clocks

Dongsheng Wu
Let X={X(t), t[is-an-element-of][openface R]} be an (N, d)-fractional Brownian sheet run with nonlinear clocks, that is, X(t) = B(F(t), …, F(t)) for all t=(t,...,t)[is-an-element-of][openface R], where B is an (N, d)-fractional Brownian sheet with Hurst indices H = (H, …, H) [is-an-el ... [J. Math. Phys. 53, 013514 (2012)] published Fri Jan 20, 2012.

Circular law and arc law for truncation of random unitary matrix

Zhishan Dong, Tiefeng Jiang, and Danning Li
Let V be the m x m upper-left corner of an n x n Haar-invariant unitary matrix. Let lambda, …, lambda be the eigenvalues of V. We prove that the empirical distribution of a normalization of lambda, …, lambda goes to the circular law, that is, the uniform distribution on {z[is-an-el ... [J. Math. Phys. 53, 013301 (2012)] published Fri Jan 20, 2012.

Spinor representation for loop quantum gravity

Etera Livine and Johannes Tambornino
We perform a quantization of the loop gravity phase space purely in terms of spinorial variables, which have recently been shown to provide a direct link between spin network states and simplicial geometries. The natural Hilbert space to represent these spinors is the Bargmann space of holomorphic s ... [J. Math. Phys. 53, 012503 (2012)] published Fri Jan 20, 2012.

On the transition from microscopic to macroscopic electrodynamics

O. L. de Lange, R. E. Raab, and A. Welter
Implicit in the change from microscopic electrodynamics to a macroscopic, multipole theory is a set of molecule-fixed coordinate systems and hence an arbitrary set of molecular origins {O} relative to which the positions of molecular constituents are specified. We examine the extent to which this ... [J. Math. Phys. 53, 013513 (2012)] published Fri Jan 20, 2012.

Global existence and asymptotic behavior of solutions to a nonlinear wave equation of fourth-order

Yu-Zhu Wang and Yin-Xia Wang
In this paper we focus on the Cauchy problem for a nonlinear wave equation of fourth-order in n-dimensional space (n >= 1), the decay structure of which is of regularity-loss property. Based on the decay estimate of solutions to the linear problem, we introduce a set of time-weighted Sobolev spaces. ... [J. Math. Phys. 53, 013512 (2012)] published Thu Jan 19, 2012.

New symbolic tools for differential geometry, gravitation, and field theory

I. M. Anderson and C. G. Torre
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combin ... [J. Math. Phys. 53, 013511 (2012)] published Wed Jan 18, 2012.

Soliton cellular automaton associated with G crystal base

Kailash C. Misra, Masato Okado, and Evan A. Wilson
We calculate the combinatorial R matrix for all elements of [script B][direct-product][script B] where [script B] denotes the G-perfect crystal of level l, and then study the soliton cellular automaton constructed from it. The solitons of length l are identified with elements of the A-crystal [scrip ... [J. Math. Phys. 53, 013510 (2012)] published Wed Jan 18, 2012.

Generalization of H-pseudoalgebraic structures

Qinxiu Sun
The goal of this paper is to study Hom-H-pseudoalgebraic structures generalizing H-pseudoalgebras of associative and Lie type. We provide examples of the new structures and present some properties and construction theorems. Similar to the case of H-pseudoalgebras, the annihilator algebras are also d ... [J. Math. Phys. 53, 012105 (2012)] published Wed Jan 18, 2012.

Notes on the Riccati operator equation in open quantum systems

Bartlomiej Gardas and Zbigniew Puchala
A recent problem [B. Gardas, J. Math. Phys. 52, 042104 (2011)] concerning an antilinear solution of the Riccati equation is solved. We also exemplify that a simplification of the Riccati equation, even under reasonable assumptions, can lead to a not equivalent equation. ... [J. Math. Phys. 53, 012106 (2012)] published Wed Jan 18, 2012.

Fourier, Gauss, Fraunhofer, Porod and the shape from moments problem

Gregg M. Gallatin
We show how the Fourier transform of a shape in any number of dimensions can be simplified using Gauss's law and evaluated explicitly for polygons in two dimensions, polyhedra in three dimensions, etc. We also show how this combination of Fourier and Gauss can be related to numerous classical proble ... [J. Math. Phys. 53, 013509 (2012)] published Tue Jan 17, 2012.

Compound transfer matrices: Constructive and destructive interference

Petarpa Boonserm and Matt Visser
Scattering from a compound barrier, one composed of a number of distinct non-overlapping sub-barriers, has a number of interesting and subtle mathematical features. If one is scattering classical particles, where the wave aspects of the particle can be ignored, the transmission probability of the co ... [J. Math. Phys. 53, 012104 (2012)] published Tue Jan 17, 2012.

The Biot-Savart operator and electrodynamics on subdomains of the three-sphere

Jason Parsley
We study steady-state magnetic fields in the geometric setting of positive curvature on subdomains of the three-dimensional sphere. By generalizing the Biot-Savart law to an integral operator BS acting on all vector fields, we show that electrodynamics in such a setting behaves rather similarly to E ... [J. Math. Phys. 53, 013102 (2012)] published Fri Jan 13, 2012.

Vortex dynamics in [openface R]

Banavara N. Shashikanth
The vortex dynamics of Euler's equations for a constant density fluid flow in [openface R] is studied. Most of the paper focuses on singular Dirac delta distributions of the vorticity two-form omega in [openface R]. These distributions are supported on two-dimensional surfaces termed membranes and a ... [J. Math. Phys. 53, 013103 (2012)] published Fri Jan 13, 2012.

Quantum field theory on quantized Bergman domain

H. Grosse, P. Presnajder, and Zhituo Wang
We present an oscillator realization of discrete series representations of group SU(2, 2). We give formulas for the coherent state star-product quantization of a Bergman domain D. A formulation of a (regularized) noncommutative scalar field on a quantized D is given. ... [J. Math. Phys. 53, 013508 (2012)] published Fri Jan 13, 2012.

Limitations on cloning in classical mechanics

Aaron Fenyes
In this paper, we show that a result precisely analogous to the traditional quantum no-cloning theorem holds in classical mechanics. This classical no-cloning theorem does not prohibit classical cloning, we argue, because it is based on a too-restrictive definition of cloning. Using a less popular, ... [J. Math. Phys. 53, 012902 (2012)] published Thu Jan 12, 2012.

Linear differential equations and multiple zeta-values. III. Zeta(3)

Michal Zakrzewski and Henryk Zoladek
We consider the hypergeometric equation (1 t)[partial-derivative]t[partial-derivative]t[partial-derivative]g + xg = 0, whose unique analytic solution [cursive phi](t; x) = 1 + O(t) near t = 0 for t = 1 becomes a generating function for multiple zeta values [cursive phi](1; x) = f(x) = 1 zeta(3)x + ... [J. Math. Phys. 53, 013507 (2012)] published Thu Jan 12, 2012.