Journal of Mathematical Physics: All Topics

Asymptotic behavior for logarithmic diffusion

F. Salvarani
In this paper we prove, via the entropy dissipation method, that the solutions of the d-dimensional logarithmic diffusion equation, with nonhomogeneous Dirichlet boundary data, decay exponentially in time toward its own steady state. The result is valid not only in L-norm (as customary when applying ... [J. Math. Phys. 50, 113518 (2009)] published Fri Nov 20, 2009.

Markov property of Gaussian states of canonical commutation relation algebras

Denes Petz and Jozsef Pitrik
The Markov property of Gaussian states of canonical commutation relation algebras is studied. The detailed description is given by the representing block matrix. The proof is short and allows infinite dimension. The relation to classical Gaussian Markov triplets is also described. The minimizer of r ... [J. Math. Phys. 50, 113517 (2009)] published Thu Nov 19, 2009.

On some properties of orthogonal Weingarten functions

Benoit Collins and Sho Matsumoto
We give a Fourier-type formula for computing the orthogonal Weingarten formula. The Weingarten calculus was introduced as a systematic method to compute integrals of polynomials with respect to Haar measure over classical groups. Although a Fourier-type formula was known in the unitary case, the ort ... [J. Math. Phys. 50, 113516 (2009)] published Wed Nov 18, 2009.

Clebsch parameterization: Basic properties and remarks on its applications

Z. Yoshida
The Clebsch parameterization (u=[del][cursive phi]+alpha[del]beta) has advantages in elucidating structural properties of vector fields; for example, it helps formulating the Hamiltonian form of ideal fluid mechanics, representing topological constraints (Casimir invariants), integrating the Cauchy ... [J. Math. Phys. 50, 113101 (2009)] published Wed Nov 18, 2009.

Erratum: Geometric prequantization of the moduli space of the vortex equations on a Riemann surface [J. Math. Phys. 47, 103501 (2006)]

Rukmini Dey
In this erratum to a work done previously, we give an alternative description for the prequantization with respect to the forms Omega, where we do not need the 1-form theta which may not be globally defined. Next by modifying the Quillen metric of the usual determinant bundle suitably, we quantize t ... [J. Math. Phys. 50, 119901 (2009)] published Tue Nov 17, 2009.

Well-posedness of Einstein's equation with redshift data

Christopher J. Winfield
We study the solvability of a system of ordinary differential equations derived from null geodesics of the LemaitreTolmanBondi metric with data given in terms of a so-called redshift parameter. Data are introduced along these geodesics by the luminosity distance function. We check our results with l ... [J. Math. Phys. 50, 113515 (2009)] published Tue Nov 17, 2009.

Deformations of 3-algebras

Jose Miguel Figueroa-O'Farrill
We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on the case of n=3 and explore the deformations of 3-algebras ... [J. Math. Phys. 50, 113514 (2009)] published Tue Nov 17, 2009.

Some applications of the fractional Poisson probability distribution

Nick Laskin
Physical and mathematical applications of the recently invented fractional Poisson probability distribution have been presented. As a physical application, a new family of quantum coherent states has been introduced and studied. As mathematical applications, we have developed the fractional generali ... [J. Math. Phys. 50, 113513 (2009)] published Mon Nov 16, 2009.

Boundary Lax pairs from non-ultra-local Poisson algebras

Jean Avan and Anastasia Doikou
We consider non-ultra-local linear Poisson algebras on a continuous line. Suitable combinations of representations of these algebras yield representations of novel generalized linear Poisson algebras or boundary extensions. They are parametrized by a boundary scalar matrix and depend, in addition, o ... [J. Math. Phys. 50, 113512 (2009)] published Fri Nov 13, 2009.

Ground states of the massless DerezinskiGerard model

Atsushi Ohkubo
We consider the massless DerezinskiGerard model introduced by Derezinski and Gerard in 1999. We give a sufficient condition for the existence of a ground state of the massless DerezinskiGerard model without the assumption that the Hamiltonian of particles has compact resolvent. ... [J. Math. Phys. 50, 113511 (2009)] published Fri Nov 13, 2009.

A practical use of the Melnikov homoclinic method

Cesar Castilho and Marcelo Marchesin
Using cutoff functions and periodic extensions, we prove that the Melnikov homoclinic method gives a criterium to show that for a finite time interval [T,T], with T arbitrarily large, the perturbed system is conjugated to a chaotic one for quite general classes of perturbation functions. The method ... [J. Math. Phys. 50, 112704 (2009)] published Fri Nov 13, 2009.

Periodic solutions on the SturmLiouville boundary value problem for two-dimensional wave equation

Shuguan Ji
In this paper, we study the periodic solutions to two-dimensional wave equation yDeltay+ay+g(y)=f(x,t) on (0,pi) x (0,pi) x [openface R] under the periodic conditions y(x,t+T)=y(x,t), y(x,t+T)=y(x,t), and the SturmLiouville boundary conditions ay(0,x,t)by(0,x,t)=0, ay(pi,x,t)+by(pi,x,t)=0, ay(x,0,t) ... [J. Math. Phys. 50, 113510 (2009)] published Thu Nov 12, 2009.

Characterization of partial positive transposition states and measures of entanglement

Wladyslaw A. Majewski, Takashi Matsuoka, and Masanori Ohya
A detailed characterization of partial positive transposition (PPT) states, both in the Heisenberg and in the Schrodinger picture, is given. Measures of entanglement are defined and discussed in details. Illustrative examples are provided. ... [J. Math. Phys. 50, 113509 (2009)] published Thu Nov 12, 2009.

Dynamical systems and Poisson structures

Metin Gurses, Gusein Sh. Guseinov, and Kostyantyn Zheltukhin
We first consider the Hamiltonian formulation of n=3 systems, in general, and show that all dynamical systems in [openface R] are locally bi-Hamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical system. The construction of the Poisson structures is based on solvin ... [J. Math. Phys. 50, 112703 (2009)] published Thu Nov 12, 2009.

The method of Ostrogradsky, quantization, and a move toward a ghost-free future

M C Nucci and P G L Leach
The method of Ostrogradsky has been used to construct a first-order Lagrangian, hence Hamiltonian, for the fourth-order field-theoretical model of PaisUhlenbeck with unfortunate results when quantization is undertaken since states with negative norm, commonly called ghosts, appear. We propose an alt ... [J. Math. Phys. 50, 113508 (2009)] published Tue Nov 10, 2009.

Generalized log-likelihood functions and Bregman divergences

Tatsuaki Wada
Based on a two-parameter generalization of Gauss' law of error, a generalized log-likelihood is related to a Bregman divergence. This relation is a two-parameter generalization of the well-known relation between log-likelihood and KullbackLeibler divergence. ... [J. Math. Phys. 50, 113301 (2009)] published Tue Nov 10, 2009.

A note on superlinear Hamiltonian elliptic systems

Fukun Zhao, Leiga Zhao, and Yanheng Ding
This paper is concerned with the superlinear periodic elliptic systems of Hamiltonian type in the whole space. The existence of a ground state solution as well as an infinite number of geometrically distinct solutions is obtained. ... [J. Math. Phys. 50, 112702 (2009)] published Tue Nov 10, 2009.

Angular normal modes of a circular Coulomb cluster

L. W. Lupinski and M. J. Madsen
We investigate the angular normal modes for small oscillations about an equilibrium of a single-component Coulomb cluster confined by a radially symmetric external potential to a circle. The dynamical matrix for this system is a Laplacian symmetrically circulant matrix and this result leads to an an ... [J. Math. Phys. 50, 112902 (2009)] published Mon Nov 9, 2009.

Quantum scattering of relativistic particles in SafkoWitten spacetime

Herondy F. S. Mota and V. B. Bezerra
Relativistic quantum particles are considered in the background gravitational field due to a tubular matter source with an axial interior magnetic field and a vanishing exterior magnetic field, which is a solution of the combined EinsteinMaxwell fields with cylindrical symmetry. In this background, ... [J. Math. Phys. 50, 112503 (2009)] published Mon Nov 9, 2009.

On the application of a generalized dressing method to the integration of variable-coefficient coupled Hirota equations

Ting Su, Hui-Hui Dai, and Xianguo Geng
Based on the generalized dressing method, we propose two variable-coefficient coupled Hirota equations and derive their Lax pairs. The generalized dressing method is applied to study these variable-coefficient coupled Hirota equations, from which explicit solutions of the two equations and their red ... [J. Math. Phys. 50, 113507 (2009)] published Mon Nov 9, 2009.

Pseudoduality between symmetric space sigma models

Mustafa Sarisaman
We study the pseudoduality transformation on the symmetric space sigma models. We switch the Lie group-valued pseudoduality equations to Lie algebra-valued ones, which leads to an infinite number of pseudoduality equations. We obtain an infinite number of conserved currents on the tangent bundle of ... [J. Math. Phys. 50, 112303 (2009)] published Mon Nov 9, 2009.

Multiparameter deformation theory for quantum confined systems

A. N. F. Aleixo and A. B. Balantekin
We introduce a generalized multiparameter deformation theory applicable to all supersymmetric and shape-invariant systems. Taking particular choices for the deformation factors used in the construction of the deformed ladder operators, we show that we can generalize the one-parameter quantum-deforme ... [J. Math. Phys. 50, 112103 (2009)] published Mon Nov 9, 2009.

General decay rate estimate for a viscoelastic equation with weakly nonlinear time-dependent dissipation and source terms

Wenjun Liu
A viscoelastic wave equation in canonical form with weakly nonlinear time-dependent dissipation and source terms is investigated in this paper. For a wider class of relaxation functions and without imposing any restrictive growth assumption on the damping term at the origin, we establish an explicit ... [J. Math. Phys. 50, 113506 (2009)] published Fri Nov 6, 2009.

Global existence and stability for a von Karman equations with memory in noncylindrical domains

Jong Yeoul Park and Jum Ran Kang
In this paper, we study the initial-boundary value problem for the von Karman equations inside domains with moving ends. Global existence, uniqueness of solutions, and the exponential decay to the energy are established provided the initial data are bounded. ... [J. Math. Phys. 50, 112701 (2009)] published Fri Nov 6, 2009.

On the optical theorem and non-plane-wave scattering in quantum mechanics

G. Gouesbet
In quantum mechanics, the optical theorem states that the extinction cross section is equal (within a prefactor 4pi/k, in which k is a quantum wave number) to the imaginary part of the forward scattering angular function. This theorem is valid for plane wave scattering. We discuss modifications requ ... [J. Math. Phys. 50, 112302 (2009)] published Fri Nov 6, 2009.

Particle topology, braids, and braided belts

Sundance Bilson-Thompson, Jonathan Hackett, and Louis H. Kauffman
Recent work [S. O. Bilson-Thompson, e-print arXiv:hep-th/0503213; Bilson-Thompson et al., Class. Quantum Grav. 24, 3975 (2007)] suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the first generation in th ... [J. Math. Phys. 50, 113505 (2009)] published Thu Nov 5, 2009.

On the Moyal deformation of Nahm equations in seven dimensions

Hugo Garcia-Compean and Aldo A. Martinez-Merino
We show how the reduced (anti-)self-dual YangMills equations to seven dimensions described by the Nahm equations can be carried over to the WeylWignerMoyal formalism. In the process some new solutions for the cases of gauge groups SU(2) and SL(2,[openface R]) are explicitly obtained. ... [J. Math. Phys. 50, 113504 (2009)] published Thu Nov 5, 2009.

Lorentz symmetric quantum field theory for symplectic fermions

Dean J. Robinson, Eliot Kapit, and Andre LeClair
A free quantum field theory with Lorentz symmetry is derived for spin-half symplectic fermions in 2+1 dimensions. In particular, we show that fermionic spin-half fields may be canonically quantized in a free theory with a KleinGordon Lagrangian. This theory is shown to have all the required properti ... [J. Math. Phys. 50, 112301 (2009)] published Thu Nov 5, 2009.

An extension theorem for conformal gauge singularities

Christian Lubbe and Paul Tod
We analyze conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theor ... [J. Math. Phys. 50, 112501 (2009)] published Tue Nov 3, 2009.

Integrable higher order deformations of Heisenberg supermagnetic model

Jia-Feng Guo, Shi-Kun Wang, Ke Wu, Zhao-Wen Yan, and Wei-Zhong Zhao
The Heisenberg supermagnet model is an integrable supersymmetric system and has a close relationship with the strong electron correlated Hubbard model. In this paper, we investigate the integrable higher order deformations of Heisenberg supermagnet models with two different constraints: (i) S=3S2I f ... [J. Math. Phys. 50, 113502 (2009)] published Tue Nov 3, 2009.

Analysis of unbounded operators and random motion

Palle E. T. Jorgensen
We study infinite weighted graphs with view to limits at infinity or boundaries at infinity. Examples of such weighted graphs arise in infinite (in practice, that means very large) networks of resistors or in statistical mechanics models for classical or quantum systems. However, more generally, our ... [J. Math. Phys. 50, 113503 (2009)] published Tue Nov 3, 2009.

Degenerations of pre-Lie algebras

Thomas Benes and Dietrich Burde
We consider the variety of pre-Lie algebra structures on a given n-dimensional vector space. The group GL(K) acts on it, and we study the closure of the orbits with respect to the Zariski topology. This leads to the definition of pre-Lie algebra degenerations. We give fundamental results on such deg ... [J. Math. Phys. 50, 112102 (2009)] published Tue Nov 3, 2009.

A conformal extension theorem based on null conformal geodesics

Christian Lubbe
In this article we describe the formulation of null geodesics as null conformal geodesics and their description in the tractor formalism. A conformal extension theorem through an isotropic singularity is proven by requiring the boundedness of the tractor curvature and its derivatives to sufficient o ... [J. Math. Phys. 50, 112502 (2009)] published Tue Nov 3, 2009.

On geometric perturbations of critical Schrodinger operators with a surface interaction

Pavel Exner and Martin Fraas
We study singular Schrodinger operators with an attractive interaction supported by a closed smooth surface [script A][subset or is implied by][openface R] and analyze their behavior in the vicinity of the critical situation where such an operator has empty discrete spectrum and a threshold resonanc ... [J. Math. Phys. 50, 112101 (2009)] published Tue Nov 3, 2009.

Spectral representation of infimum of bounded quantum observables

Shen Jun and Wu Junde
In 2006, Gudder [Math. Slovaca 56, 573 (2006)] introduced a logic order [curly precedes, eq] on bounded quantum observable set S(H). In 2007, Pulmannova and Vincekova [Math Slovaca 57, 589 (2007)] proved that for each subset [script D] of S(H), the infimum of [script D] exists with respect to the lo ... [J. Math. Phys. 50, 113501 (2009)] published Mon Nov 2, 2009.

Interference in the radiation of two pointlike charges

Yurij Yaremko
Energy-momentum and angular momentum carried by electromagnetic field of two pointlike charged particles arbitrarily moving in flat space-time are presented. Apart from usual contributions to the Noether quantities produced separately by particles 1 and 2, the conservation laws contain also joint co ... [J. Math. Phys. 50, 112901 (2009)] published Mon Nov 2, 2009.

Complete list of Darboux integrable chains of the form t=t+d(t,t)

Ismagil Habibullin, Natalya Zheltukhina, and Aslı Pekcan
We study differential-difference equation (d/dx)t(n+1,x)=f(t(n,x),t(n+1,x),(d/dx)t(n,x)) with unknown t(n,x) depending on continuous and discrete variables x and n. Equation of such kind is called Darboux integrable, if there exist two functions F and I of a finite number of arguments x, {t(n+k,x)}, ... [J. Math. Phys. 50, 102710 (2009)] published Fri Oct 30, 2009.

Scalar field theory in kappa-Minkowski spacetime from twist

Hyeong-Chan Kim, Youngone Lee, Chaiho Rim, and Jae Hyung Yee
Using the twist deformation of U(igl(4,R)), the linear part of the diffeomorphism, we define a scalar function and construct a free scalar field theory in four-dimensional kappa-Minkowski spacetime. The action in momentum space turns out to differ only in the integration measure from the commutative ... [J. Math. Phys. 50, 102304 (2009)] published Fri Oct 30, 2009.

Compact shell solitons in K field theories

C. Adam, P. Klimas, J. Sanchez-Guillen, and A. Wereszczynski
Some models providing shell-shaped static solutions with compact support (compactons) in 3+1 and 4+1 dimensions are introduced, and the corresponding exact solutions are calculated analytically. These solutions turn out to be topological solitons and may be classified as maps S-->S and suspended Hop ... [J. Math. Phys. 50, 102303 (2009)] published Thu Oct 29, 2009.

Explicit pure-state density operator structure for quantum tomography

Hong-yi Fan and Cui-hong Lv
The formulation of region operators named by D. Ellinas and A. J. Bracken [Phys. Rev. A 78, 052106 (2008)], which appears as the phase-space integration corresponding to the straight line over the Wigner operator, is manifestly improved and generalized. By virtue of the technique of integration with ... [J. Math. Phys. 50, 102108 (2009)] published Thu Oct 29, 2009.

On fixed points of Luders operation

Liu Weihua and Wu Junde
In this paper, we give a concrete example of a Luders operation L with n=3, such that L(B)=B does not imply that B commutes with all E, E, and E in [script A], this example answers an open problem of Professor Gudder. ... [J. Math. Phys. 50, 103531 (2009)] published Wed Oct 28, 2009.

The hot spots conjecture for a certain class of planar convex domains

Yasuhito Miyamoto
We prove the hot spots conjecture of Rauch [Five problems: An introduction to the qualitative theory of partial differential equations, Partial Differential Equations and Related Topics (Program, Tulane Univ., New Orleans, La., 1974), Lecture Notes in Mathematics (Springer, Berlin, 1975), Vol. 446, ... [J. Math. Phys. 50, 103530 (2009)] published Wed Oct 28, 2009.

Dual Lindstedt series and KolmogorovArnol'dMoser theorem

Marco Frasca
We prove that there exists a Lindstedt series that holds when a Hamiltonian is driven by a perturbation going to infinity. This series appears to be dual to a standard Lindstedt series as it can be obtained by interchanging the role of the perturbation and the unperturbed system. The existence of th ... [J. Math. Phys. 50, 102904 (2009)] published Wed Oct 28, 2009.

Comment on Existence and regularity for an energy maximization problem in two dimensions [S. Kamvissis and E. A. Rakhmanov, J. Math. Phys. 46, 083505 (2005)]

Spyridon Kamvissis
A revision of the last appendix of the paper Existence and regularity for an energy maximization problem in two dimensions by S. Kamvissis and E. A. Rakhmanov [J. Math. Phys. 46, 083505 (2005)]. ... [J. Math. Phys. 50, 104101 (2009)] published Mon Oct 26, 2009.

A conformal variational approach for helices in nature

Manuel Barros and Angel Ferrandez
We propose a two step variational principle to describe helical structures in nature. The first one is governed by an energy action which is a linear function in both curvature and torsion allowing to describe nonclosed structures including elliptical, spherical, and conical helices. These appear as ... [J. Math. Phys. 50, 103529 (2009)] published Mon Oct 26, 2009.

Second-order neutral impulsive stochastic evolution equations with delay

Yong Ren and Dandan Sun
In this paper, we study the second-order neutral stochastic evolution equations with impulsive effect and delay (SNSEEIDs). We establish the existence and uniqueness of mild solutions to SNSEEIDs under non-Lipschitz condition with Lipschitz condition being considered as a special case by the success ... [J. Math. Phys. 50, 102709 (2009)] published Mon Oct 26, 2009.