Journal of Mathematical Physics: All Topics

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.

Determination of elementary first integrals of a generalized Raychaudhuri equation by the Darboux integrability method

A. Ghose Choudhury, Partha Guha, and Barun Khanra
The Darboux integrability method is particularly useful to determine first integrals of nonplanar autonomous systems of ordinary differential equations, whose associated vector fields are polynomials. In particular, we obtain first integrals for a variant of the generalized Raychaudhuri equation, wh ... [J. Math. Phys. 50, 102502 (2009)] published Fri Oct 23, 2009.

Quantum hypothesis testing with group symmetry

Fumio Hiai, Milan Mosonyi, and Masahito Hayashi
The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with the problems of the Chernoff bound, the Hoeffding bound, an ... [J. Math. Phys. 50, 103304 (2009)] published Thu Oct 22, 2009.

On continuum dynamics

Giovanni Romano, Raffaele Barretta, and Marina Diaco
The theory of continuous dynamical systems is developed with an intrinsic geometric approach based on the action principle formulated in the velocity-time manifold. By endowing the finite dimensional Riemannian ambient manifold with a connection, an induced connection is naturally defined in the inf ... [J. Math. Phys. 50, 102903 (2009)] published Thu Oct 22, 2009.

Weyl's Lagrangian in teleparallel form

James Burnett and Dmitri Vassiliev
The Weyl Lagrangian is the massless Dirac Lagrangian. The dynamical variable in the Weyl Lagrangian is a spinor field. We provide a mathematically equivalent representation in terms of a different dynamical variable the coframe (an orthonormal tetrad of covector fields). We show that when written i ... [J. Math. Phys. 50, 102501 (2009)] published Tue Oct 20, 2009.

Closed-form evaluation of integrals appearing in positronium decay

Tewodros Amdeberhan, Victor H. Moll, and Armin Straub
A theoretical prediction for the total width of the positronium decay in quantum electrodynamics has been given by Kniehl et al. [Irrational constants in positronium decays, Nucl. Phys. B (Proc. Suppl.) 184, 14 (2008), arXiv:hep-ph/0811.0306] in the form of an expansion in Sommerfeld's fine-structur ... [J. Math. Phys. 50, 103528 (2009)] published Tue Oct 20, 2009.

No-cloning theorem on quantum logics

Takayuki Miyadera and Hideki Imai
This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only class ... [J. Math. Phys. 50, 102107 (2009)] published Tue Oct 20, 2009.

Note on the Poisson structure of the damped oscillator

A. N. W. Hone and M. Senthilvelan
The damped harmonic oscillator is one of the most studied systems with respect to the problem of quantizing dissipative systems. Recently Chandrasekar et al. [J. Math. Phys. 48, 032701 (2007)] applied the PrelleSinger method to construct conserved quantities and an explicit time-independent Lagrangi ... [J. Math. Phys. 50, 102902 (2009)] published Tue Oct 20, 2009.

Adiabatic approximation with exponential accuracy for many-body systems and quantum computation

Daniel A. Lidar, Ali T. Rezakhani, and Alioscia Hamma
We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is controllable. Assuming that the Hamiltonian is analytic in a finit ... [J. Math. Phys. 50, 102106 (2009)] published Tue Oct 20, 2009.

Time-reversal frameness and superselection

Gilad Gour, Barry C. Sanders, and Peter S. Turner
We show that appropriate superpositions of motional states are a reference frame resource that enables breaking of time-reversal superselection so that two parties lacking knowledge about the other's direction of time can still communicate. We identify the time-reversal reference frame resource stat ... [J. Math. Phys. 50, 102105 (2009)] published Mon Oct 19, 2009.

The correlation functions of plane polygons

Salvino Ciccariello
The correlation function of a bounded plane figure of arbitrary shape and its derivatives are studied using their integral expressions. From these follows that the correlation function and its first derivative are continuous functions, while the second and the higher order derivatives can show finit ... [J. Math. Phys. 50, 103527 (2009)] published Fri Oct 16, 2009.

Analysis of generalized Forchheimer flows of compressible fluids in porous media

Eugenio Aulisa, Lidia Bloshanskaya, Luan Hoang, and Akif Ibragimov
This work is focused on the analysis of nonlinear flows of slightly compressible fluids in porous media not adequately described by Darcy's law. We study a class of generalized nonlinear momentum equations which covers all three well-known Forchheimer equations, the so-called two-term, power, and th ... [J. Math. Phys. 50, 103102 (2009)] published Fri Oct 16, 2009.

Collinear central configurations in the n-body problem with general homogeneous potential

Mervin Woodlin and Zhifu Xie
In this paper we investigate the central configurations of collinear n-body problem given by the general law of attraction of the form f(r)=1/r. A method involving analysis skills of some elementary algebra and calculus is presented to study the central configurations in the collinear n-body problem ... [J. Math. Phys. 50, 102901 (2009)] published Fri Oct 16, 2009.

The nonrelativistic limit of (central-extended) Poincare group and some consequences for quantum actualization

Juan S. Ardenghi, M. Castagnino, and R. Campoamor-Stursberg
The nonrelativistic limit of the centrally extended Poincare group is considered and their consequences in the modal Hamiltonian interpretation of quantum mechanics are discussed [O. Lombardi and M. Castagnino, Stud. Hist. Philos. Mod. Phys 39, 380 (2008); J. Phys, Conf. Ser. 128, 012014 (2008)]. Th ... [J. Math. Phys. 50, 103526 (2009)] published Thu Oct 15, 2009.

Basic results on the equations of magnetohydrodynamics of partially ionized inviscid plasmas

Manuel Nunez
The equations of evolution of partially ionized plasmas have been far more studied in one of their many simplifications than in its original form. They present a relation between the velocity of each species, plus the magnetic and electric fields, which yield as an analog of Ohm's law a certain elli ... [J. Math. Phys. 50, 103101 (2009)] published Thu Oct 15, 2009.

Regularity criteria of weak solutions to the three-dimensional micropolar flows

Bo-Qing Dong and Zhi-Min Chen
Regularity criteria of weak solutions to the three-dimensional micropolar fluid motion equations are discussed. Sufficient conditions for the regularity of weak solutions are presented by imposing Serrin's type growth conditions on the velocity field in Lorentz spaces, multiplier spaces, bounded mea ... [J. Math. Phys. 50, 103525 (2009)] published Wed Oct 14, 2009.

A model for reversible reaction in a subdiffusive regime

Xicheng Li and Mingyu Xu
In this study, a model of reversible reaction in subdiffusive regime is set up by incorporating a reversible reaction term to a subdiffusion equation. Some models discussed previously are special cases of the model here and can be obtained by selecting proper parameters in the equations. Two differe ... [J. Math. Phys. 50, 102708 (2009)] published Tue Oct 13, 2009.

The fractional Schrodinger operator and Toeplitz matrices

Agapitos Hatzinikitas
Confining a quantum particle in a compact subinterval of the real line with Dirichlet boundary conditions, we identify the connection of the one-dimensional fractional Schodinger operator with the truncated Toeplitz matrices. We determine the asymptotic behavior of the product of eigenvalues for the ... [J. Math. Phys. 50, 103524 (2009)] published Fri Oct 9, 2009.

Phase separation of two-component BoseEinstein condensates

Zuhan Liu
Recently, coupled systems of nonlinear Schrodinger equations have been used extensively to describe mixtures BoseEinstein condensates. In this paper, we study the distribution of two different hyperfine spin states of a binary mixture of three dimensional BoseEinstein condensates. In a double conden ... [J. Math. Phys. 50, 102104 (2009)] published Fri Oct 9, 2009.

Integrability and superintegrability of the generalized n-level many-mode JaynesCummings and Dicke models

T. Skrypnyk
We analyze symmetries of the integrable generalizations of JaynesCummings and Dicke models associated with simple Lie algebras [fraktur g] and their reductive subalgebras [fraktur g] [T. Skrypnyk, Generalized n-level Jaynes-Cummings and Dicke models, classical rational r-matrices and nested Bethe an ... [J. Math. Phys. 50, 103523 (2009)] published Thu Oct 8, 2009.

Nonlinear stability of boundary layer solution to the Boltzmann equation with diffusive effect at the boundary

Qianzhu Tian and Jie Sun
In this paper, the stability of boundary layer solutions to the Boltzmann equation with diffusive effect at the boundary for hard sphere model is considered. When the Mach number of the far field is less than 1, the exponential decay in time is proven for linearized operator first. At last, based on ... [J. Math. Phys. 50, 103303 (2009)] published Thu Oct 8, 2009.

The Lambert W function and quantum statistics

S. R. Valluri, M. Gil, D. J. Jeffrey, and Shantanu Basu
We present some applications of the Lambert W function (W function) to the formalism of quantum statistics (QS). We consider the problem of finding extrema in terms of energy for a general QS distribution, which involves the solution of a transcendental equation in terms of the W function. We then p ... [J. Math. Phys. 50, 102103 (2009)] published Thu Oct 8, 2009.