American Institute of Physics: Journal of Mathematical Physics

Journal of Mathematical Physics: All Topics

On split Lie superalgebras
Antonio J. Calderon Martin and Jose M. Sanchez Delgado We study the structure of arbitrary split Lie superalgebras. We show that any of such superalgebras L is of the form L=[script U]+[summation]I with [script U] a subspace of the Abelian (graded) subalgebra H and any I, a well described (graded) ideal of L satisfying [I,I]=0 if j[not-equal]k. Under ce ... [J. Math. Phys. 51, 073511 (2010)] published Fri Jul 30, 2010.
WhittakerHill equation and semifinite-gap Schrodinger operators
A. D. Hemery and A. P. Veselov A periodic one-dimensional Schrodinger operator is called semifinite gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schrodinger operators in trigonometric functions by applying Darboux transformations to the WhittakerHill equation. We g ... [J. Math. Phys. 51, 072108 (2010)] published Thu Jul 29, 2010.
Self-dual Einstein spaces, heavenly metrics, and twistors
Sergei Alexandrov, Boris Pioline, and Stefan Vandoren Four-dimensional quaternion-Kahler metrics, or equivalently self-dual Einstein spaces [script M], are known to be encoded locally into one real function h subject to Przanowski's heavenly equation. We elucidate the relation between this description and the usual twistor description for quaternion-Ka ... [J. Math. Phys. 51, 073510 (2010)] published Wed Jul 28, 2010.
Spectral resolution of the Liouvillian of the Lindblad master equation for a harmonic oscillator
Daigo Honda, Hiromichi Nakazato, and Motoyuki Yoshida A Lindblad master equation for a harmonic oscillator, which describes the dynamics of an open system, is formally solved. The solution yields the spectral resolution of the Liouvillian, that is, all eigenvalues and eigenprojections are obtained. This spectral resolution is discussed in depth in the ... [J. Math. Phys. 51, 072107 (2010)] published Wed Jul 28, 2010.
L stability of solutions of Boltzmann equation with external force in soft potentials
Chi Honn Cheng In this paper, we present a uniform L stability theory for the solutions to Boltzmann equation with small or large external forces in vacuum in soft potentials. We assume that the initial data are sufficiently small and a fast decay in space and velocity. Our stability analysis is divided into two p ... [J. Math. Phys. 51, 073303 (2010)] published Wed Jul 28, 2010.
Two-dimensional symmetric and antisymmetric generalizations of sine functions
Jiri Hrivnak, Lenka Motlochova, and Jiri Patera The properties of two-dimensional generalizations of sine functions that are symmetric or antisymmetric with respect to permutations of their two variables are described. It is shown that the functions are orthogonal when integrated over a finite region F of the real Euclidean space, and that they a ... [J. Math. Phys. 51, 073509 (2010)] published Wed Jul 28, 2010.
Matrix pencils and entanglement classification
Eric Chitambar, Carl A. Miller, and Yaoyun Shi Quantum entanglement plays a central role in quantum information processing. A main objective of the theory is to classify different types of entanglement according to their interconvertibility through manipulations that do not require additional entanglement to perform. While bipartite entanglement ... [J. Math. Phys. 51, 072205 (2010)] published Thu Jul 22, 2010.
Cylindrically symmetric vacuum solutions in higher dimensional BransDicke theory
Ahmet Baykal, Dilek K. Ciftci, and Ozgur Delice Higher dimensional, static, cylindrically symmetric vacuum solutions with and without a cosmological constant in the BransDicke theory are presented. We show that for a negative cosmological constant and for specific values of the parameters, a particular subclass of these solutions includes higher ... [J. Math. Phys. 51, 072505 (2010)] published Wed Jul 21, 2010.
Exponential error rates in multiple state discrimination on a quantum spin chain
Michael Nussbaum and Arleta Szkola We consider decision problems on finite sets of hypotheses represented by pairwise different shift-invariant states on a quantum spin chain. The decision in favor of one of the hypotheses is based on outcomes of generalized measurements performed on local states on blocks of finite size. We assume t ... [J. Math. Phys. 51, 072203 (2010)] published Wed Jul 21, 2010.
Householder factorizations of unitary matrices
Jesus Urias A method to construct all representations of finite dimensional unitary matrices as the product of Householder reflections is given. By arbitrarily severing the state space into orthogonal subspaces, the method may, e.g., identify the entangling and single-component quantum operations that are requi ... [J. Math. Phys. 51, 072204 (2010)] published Wed Jul 21, 2010.
YangMills equations of motion for the Higgs sector of SU(3)-equivariant quiver gauge theories
Thorsten Rahn We consider SU(3)-equivariant dimensional reduction of YangMills theory on spaces of the form [openface R] x SU(3)/H, with H equals either SU(2) x U(1) or U(1) x U(1). For the corresponding quiver gauge theory, we derive the equations of motion and construct some specific solutions for the Higgs fie ... [J. Math. Phys. 51, 072302 (2010)] published Wed Jul 21, 2010.
From golden spirals to constant slope surfaces
Marian Ioan Munteanu In this paper, we find all constant slope surfaces in the Euclidean 3-space, namely, those surfaces for which the position vector of a point of the surface makes constant angle with the normal at the surface in that point. These surfaces could be thought as the bidimensional analog of the generalize ... [J. Math. Phys. 51, 073507 (2010)] published Tue Jul 20, 2010.
General decay for a nonlinear beam equation with weak dissipation
Jong Yeoul Park and Sun Hye Park In this paper, we investigate the influence of dissipation on decay properties of the solutions for a quasilinear beam equation with nonlinear weak dissipation. ... [J. Math. Phys. 51, 073508 (2010)] published Tue Jul 20, 2010.
An extended noncommutative KP hierarchy
Wen-Xiu Ma Introducing squared eigenfunctions in the Moyal-deformed Lax equations generates an extended noncommutative KP (ncKP) hierarchy. The compatibility equations between the ncKP flows and the extended ncKP flows and the compatibility equations among the extended ncKP flows themselves are constructed. Th ... [J. Math. Phys. 51, 073505 (2010)] published Mon Jul 19, 2010.
A decay result to a viscoelastic problem in [openface R] with an oscillating kernel
Mohammad Kafini and Nasser-eddine Tatar In this paper we consider a linear Cauchy viscoelastic problem. We show that, for compactly supported initial data and for not necessarily decreasing (oscillating) relaxation function, the decay of the first energy of solutions is polynomial. The proof relies on some appropriately chosen functionals ... [J. Math. Phys. 51, 073506 (2010)] published Mon Jul 19, 2010.
Asymptotic expansion of the log-partition function for a gas of interacting Brownian loops. II.
Suren Poghosyan In an earlier paper [Poghosyan, S. and Zessin, H., Asymptotic expansion of the log-partition function for a gas of interacting Brownian loops, J. Math. Phys. 48, 093301 (2007)] we studied the asymptotic expansion of the log-partition function of a quantum gas in a bounded domain as this domain is di ... [J. Math. Phys. 51, 073302 (2010)] published Mon Jul 19, 2010.
Hadamard matrices from mutually unbiased bases
P. Dita An analytical method for getting new complex Hadamard matrices by using mutually unbiased bases and a nonlinear doubling formula is provided. The method is illustrated with the n=4 case that leads to a rich family of eight-dimensional Hadamard matrices that depend on five arbitrary parameters whose ... [J. Math. Phys. 51, 072202 (2010)] published Mon Jul 19, 2010.
The Hamiltonian formulation for the dynamics of a multishell self-gravitating system
J. Kijowski, G. Magli, and D. Malafarina Hamiltonian function describing a system composed of n gravitating shells in general relativity is derived from general considerations and its dynamics is presented. The results appear to be promising for the description of colliding system of astrophysical and cosmological interest. ... [J. Math. Phys. 51, 072504 (2010)] published Mon Jul 19, 2010.
Construction of classical superintegrable systems with higher order integrals of motion from ladder operators
Ian Marquette We construct integrals of motion for multidimensional classical systems from ladder operators of one-dimensional systems. This method can be used to obtain new systems with higher order integrals. We show how these integrals generate a polynomial Poisson algebra. We consider a one-dimensional system ... [J. Math. Phys. 51, 072903 (2010)] published Mon Jul 19, 2010.
Conservative solutions for higher-order CamassaHolm equations
Danping Ding and Peng Lv This paper studies the existence of global solutions to higher-order CamassaHolm equations. Global solution is constructed by the small viscosity method for the frequency localized equation, especially global solution is energy conservative for given finite band initial data. ... [J. Math. Phys. 51, 072701 (2010)] published Fri Jul 16, 2010.
Order-dependent mappings: Strong-coupling behavior from weak-coupling expansions in non-Hermitian theories
Jean Zinn-Justin and Ulrich D. Jentschura A long time ago, it has been conjectured that a Hamiltonian with a potential of the form x+ivx, v real, has a real spectrum. This conjecture has been generalized to a class of the so-called [script P][script T] symmetric Hamiltonians and some proofs have been given. Here, we show by numerical invest ... [J. Math. Phys. 51, 072106 (2010)] published Fri Jul 16, 2010.
Mixed potentials in radiative stellar collapse
S. Thirukkanesh and S. D. Maharaj We study the behavior of a radiating star when the interior expanding, shearing fluid particles are traveling in geodesic motion. We demonstrate that it is possible to obtain new classes of exact solutions in terms of elementary functions without assuming a separable form for the gravitational poten ... [J. Math. Phys. 51, 072502 (2010)] published Fri Jul 16, 2010.
de Sitter breaking through infrared divergences
S. P. Miao, N. C. Tsamis, and R. P. Woodard Just because the propagator of some field obeys a de Sitter invariant equation does not mean it possesses a de Sitter invariant solution. The classic example is the propagator of a massless, minimally coupled scalar. We show that the same thing happens for massive scalars with M<0 and for massive tr ... [J. Math. Phys. 51, 072503 (2010)] published Fri Jul 16, 2010.
Tree expansion in time-dependent perturbation theory
Christian Brouder, Angela Mestre, and Frederic Patras The computational complexity of time-dependent perturbation theory is well known to be largely combinatorial whatever the chosen expansion method and family of parameters (combinatorial sequences, Goldstone and other Feynman-type diagrams, etc.). We show that a very efficient perturbative expansion, ... [J. Math. Phys. 51, 072104 (2010)] published Thu Jul 15, 2010.
Maximal violation of Bell inequalities by position measurements
J. Kiukas and R. F. Werner We show that it is possible to find maximal violations of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality using only position measurements on a pair of entangled nonrelativistic free particles. The device settings required in the CHSH inequality are done by choosing one of two times at which p ... [J. Math. Phys. 51, 072105 (2010)] published Thu Jul 15, 2010.
Infinite-dimensional symmetries of two-dimensional generalized Burgers equations
F. Gungor The conditions for a class of generalized Burgers equations which a priori involve nine arbitrary functions of one or two variables to allow an infinite-dimensional symmetry algebra are determined. Although this algebra can involve up to two arbitrary functions of time, it does not allow a Virasoro ... [J. Math. Phys. 51, 073504 (2010)] published Thu Jul 15, 2010.
Classification of two and three dimensional Lie superbialgebras
A. Eghbali, A. Rezaei-Aghdam, and F. Heidarpour Using adjoint representation of Lie superalgebras, we obtain the matrix form of super-Jacobi and mixed super-Jacobi identities of Lie superbialgebras. By direct calculations of these identities, and use of automorphism supergroups of two and three dimensional Lie superalgebras, we obtain and classif ... [J. Math. Phys. 51, 073503 (2010)] published Thu Jul 15, 2010.
Correlation of Dirac potentials and atomic inversion in cavity quantum electrodynamics
Agung Trisetyarso Controlling the time evolution of the population of two states in cavity quantum electrodynamics is necessary by tuning the modified Rabi frequency in which the extra classical effect of electromagnetic field is taken into account. The theoretical explanation underlying the perturbation of potential ... [J. Math. Phys. 51, 072103 (2010)] published Thu Jul 15, 2010.
Conjugate degradability and the quantum capacity of cloning channels
Kamil Bradler, Nicolas Dutil, Patrick Hayden, and Abubakr Muhammad A quantum channel is conjugate degradable if the channel's environment can be simulated up to complex conjugation using the channel's output. For all such channels, the quantum capacity can be evaluated using a single-letter formula. In this article we introduce conjugate degradability and establish ... [J. Math. Phys. 51, 072201 (2010)] published Thu Jul 15, 2010.
An expansion of the homoclinic splitting matrix for the rapidly, quasiperiodically, forced pendulum
Mikko Stenlund We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, devising an expansion for the splitting matrix associated with a homoclinic point. This expansion consists of contributions that are manifestly exponentially small in the limit of vanishing hyperbolicity by ... [J. Math. Phys. 51, 072902 (2010)] published Thu Jul 15, 2010.
The causal perturbation expansion revisited: Rescaling the interacting Dirac sea
Felix Finster and Andreas Grotz The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contain ... [J. Math. Phys. 51, 072301 (2010)] published Tue Jul 13, 2010.
Linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold
Romain Gicquaud We study the linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold. In particular, we prove that these equations are linearization stable in the neighborhood of vacuum solutions for a nonpositive cosmological constant and of FriedmanLemaitreRobertsonWa ... [J. Math. Phys. 51, 072501 (2010)] published Fri Jul 9, 2010.
Photon scattering in geometrical optics
Wilhelm von Waldenfels A quasimonochromatic wave packet is scattered by a system of two level atoms. The transition frequency of atoms coincides with the frequency of the wave packet, their distances are proportional to that frequency. The time evolution can be calculated explicitly. Using FourierWeyl transform and after ... [J. Math. Phys. 51, 072901 (2010)] published Fri Jul 9, 2010.
On locally and nonlocally related potential systems
Alexei F. Cheviakov and George W. Bluman For any partial differential equation (PDE) system, a local conservation law yields potential equations in terms of some potential variable, which normally is a nonlocal variable. The current paper examines situations when such a potential variable is a local variable, i.e., is a function of the ind ... [J. Math. Phys. 51, 073502 (2010)] published Fri Jul 9, 2010.
A generalized coupled Kortewegde Vries hierarchy, bi-Hamiltonian structure, and Darboux transformation
Zhaqilao and Sirendaoreji A new generalized coupled Kortewegde Vries (KdV) hierarchy is presented starting from a 4 x 4 matrix spectral problem with four potentials. Its generalized bi-Hamiltonian structure is also investigated by using the trace identity. Most importantly, a new generalized coupled KdV equation is produced. ... [J. Math. Phys. 51, 073501 (2010)] published Thu Jul 8, 2010.
A generalization of the cumulant expansion. Application to a scale-invariant probabilistic model
A. Rodriguez and C. Tsallis As well known, cumulant expansion is an alternative way to moment expansion to fully characterize probability distributions provided all the moments exist. If this is not the case, the so-called escort mean values (or q-moments) have been proposed to characterize probability densities with divergent ... [J. Math. Phys. 51, 073301 (2010)] published Tue Jul 6, 2010.
A deformation quantization theory for noncommutative quantum mechanics
Nuno Costa Dias, Maurice de Gosson, Franz Luef, and Joao Nuno Prata We show that the deformation quantization of noncommutative quantum mechanics previously considered by Dias and Prata [WeylWigner formulation of noncommutative quantum mechanics, J. Math. Phys. 49, 072101 (2008)] and Bastos, Dias, and Prata [Wigner measures in non-commutative quantum mechanics, e-pr ... [J. Math. Phys. 51, 072101 (2010)] published Fri Jul 2, 2010.
The geometric measure of multipartite entanglement and the singular values of a hypermatrix
Joseph J. Hilling and Anthony Sudbery It is shown that the geometric measure of entanglement of a pure multipartite state satisfies a polynomial equation, generalizing the singular-value equation of the matrix of coefficients of a bipartite state. The equation is solved for a class of three-qubit states. ... [J. Math. Phys. 51, 072102 (2010)] published Fri Jul 2, 2010.