Journal of Mathematical Physics: All Topics

On the relationship between the classical Dicke-Jaynes-Cummings-Gaudin model and the nonlinear Schrodinger equation

Dianlou Du and Xue Geng
In this paper, the relationship between the classical Dicke-Jaynes-Cummings-Gaudin (DJCG) model and the nonlinear Schrodinger (NLS) equation is studied. It is shown that the classical DJCG model is equivalent to a stationary NLS equation. Moreover, the standard NLS equation can be solved by the clas ... [J. Math. Phys. 54, 053510 (2013)] published Fri May 17, 2013.

The two dimensional motion of a particle in an inverse square potential: Classical and quantum aspects

R. P. Martinez-y-Romero, H. N. Nunez-Yepez, and A. L. Salas-Brito
The classical 2D dynamics of a particle moving under an inverse square potential, k/r, is analysed. We show that such problem is an example of a geometric system since its negative energy orbits are equivalent to free motion on a certain hypersurface. We then solve in momentum space, the correspondi ... [J. Math. Phys. 54, 053509 (2013)] published Fri May 17, 2013.

Analytical solutions of the Schrodinger equation for a two-dimensional exciton in magnetic field of arbitrary strength

Ngoc-Tram Hoang-Do, Van-Hung Hoang, and Van-Hoang Le
The Feranchuk-Komarov operator method is developed by combining with the Levi-Civita transformation in order to construct analytical solutions of the Schrodinger equation for a two-dimensional exciton in a uniform magnetic field of arbitrary strength. As a result, analytical expressions for the ener ... [J. Math. Phys. 54, 052105 (2013)] published Thu May 16, 2013.

Thermal nonlinear coherent states on a flat space and on a sphere

H. Bagheri and A. Mahdifar
In this paper, we first define thermal nonlinear coherent states on a sphere and show that these states are essentially two-mode squeezed nonlinear coherent states of the sphere at zero temperature. Then we consider quantum statistical properties of the thermal sphere nonlinear coherent states. In p ... [J. Math. Phys. 54, 052104 (2013)] published Wed May 15, 2013.

A reduction theorem for time dependent Schrodinger operator with finite differentiable unbounded perturbation

Xiaoping Yuan and Kangkang Zhang
In this paper, we consider the time dependent Schrodinger operator with a temporal quasi-periodic perturbation which is some function of class C for any [script-l] >= 100(3n + 2tau + 1), by using the KAM technique, we establish a reduction theorem for the above operator and prove that the invariant ... [J. Math. Phys. 54, 052701 (2013)] published Wed May 15, 2013.

Real second order freeness and Haar orthogonal matrices

James A. Mingo and Mihai Popa
We demonstrate the asymptotic real second order freeness of Haar distributed orthogonal matrices and an independent ensemble of random matrices. Our main result states that if we have two independent ensembles of random matrices with a real second order limit distribution and one of them is invarian ... [J. Math. Phys. 54, 051701 (2013)] published Tue May 14, 2013.

Lie algebras and Hamiltonian structures of multi-component AblowitzKaupNewellSegur hierarchy

Xiao-ying Zhu and Da-jun Zhang
Isospectral and non-isospectral hierarchies of multi-component AblowitzKaupNewellSegur (AKNS) are obtained from a matrix spectral problem, then by means of the zero curvature representations of the isospectral flows {K} and non-isospectral flows {sigma}, we construct the symmetries and their algebra ... [J. Math. Phys. 54, 053508 (2013)] published Mon May 13, 2013.

Spherical Schrodinger operators with delta-type interactions

Sergio Albeverio, Aleksey Kostenko, Mark Malamud, and Hagen Neidhardt
We investigate spectral properties of spherical Schrodinger operators (also known as Bessel operators) with delta-point interactions concentrated on a discrete set. We obtain necessary and sufficient conditions for these Hamiltonians to be self-adjoint, lower-semibounded and also we investigate thei ... [J. Math. Phys. 54, 052103 (2013)] published Mon May 13, 2013.

Approximately clean quantum probability measures

Douglas Farenick, Remus Floricel, and Sarah Plosker
A quantum probability measureor quantum measurementis said to be clean if it cannot be irreversibly connected to any other quantum probability measure via a quantum channel. The notion of a clean quantum measure was introduced by Buscemi et al. [Clean positive operator valued measures, J. Math. Phys ... [J. Math. Phys. 54, 052201 (2013)] published Fri May 10, 2013.

The multi-dimensional Hamiltonian structures in the Whitham method

A. Ya. Maltsev
We consider the averaging of local field-theoretic Poisson brackets in the multi-dimensional case. As a result, we construct a local Poisson bracket for the regular Whitham system in the multidimensional situation. The procedure is based on the procedure of averaging of local conservation laws and f ... [J. Math. Phys. 54, 053507 (2013)] published Thu May 9, 2013.

A decomposition of irreversible diffusion processes without detailed balance

Hong Qian
As a generalization of deterministic, nonlinear conservative dynamical systems, a notion of canonical conservative dynamics with respect to a positive, differentiable stationary density rho(x) is introduced: x-dot =j(x) in which [del](rho(x)j(x)) = 0. Such systems have a conserved generalized free e ... [J. Math. Phys. 54, 053302 (2013)] published Wed May 8, 2013.

On the strong solutions of one-dimensional Navier-Stokes-Poisson equations for compressible non-Newtonian fluids

Yukun Song, Hongjun Yuan, and Yang Chen
We study the strong solutions of 1D Navier-Stokes-Poisson equations for compressible non-Newtonian fluids in bounded intervals. The model is raised from the viscous isentropic gas flow under considering an external force and the non-Newtonian gravitational force term. By using the iterative method w ... [J. Math. Phys. 54, 051502 (2013)] published Wed May 8, 2013.

Lifting general relativity to observer space

Steffen Gielen and Derek K. Wise
The observer space of a Lorentzian spacetime is the space of future-timelike unit tangent vectors. Using Cartan geometry, we first study the structure a given spacetime induces on its observer space, then use this to define abstract observer space geometries for which no underlying spacetime is assu ... [J. Math. Phys. 54, 052501 (2013)] published Tue May 7, 2013.

Exact wave solutions for BoseEinstein condensates with time-dependent scattering length and spatiotemporal complicated potential

E. Kengne, A. Lakhssassi, R. Vaillancourt, and Wu-Ming Liu
We consider a cubic-quintic GrossPitaevskii equation which governs the dynamics of BoseEinstein condensate matter waves with time-dependent scattering length and spatiotemporal complex potential. By introducing phase-imprint parameters in the system, we present the integrable condition for the equat ... [J. Math. Phys. 54, 051501 (2013)] published Tue May 7, 2013.

Classification of Lie point symmetries for quadratic Lienard type equation x-double_dot +f(x)x-dot+g(x)=0

Ajey K. Tiwari, S. N. Pandey, M. Senthilvelan, and M. Lakshmanan
In this paper we carry out a complete classification of the Lie point symmetry groups associated with the quadratic Lienard type equation, x-double_dot +f(x)x-dot+g(x)=0, where f(x) and g(x) are arbitrary functions of x. The symmetry analysis gets divided into two cases, (i) the maximal (eight param ... [J. Math. Phys. 54, 053506 (2013)] published Tue May 7, 2013.

Effective complex permittivity tensor of a periodic array of cylinders

Yuri A. Godin
We determine the effective complex permittivity of a two-dimensional composite, consisting of an arbitrary doubly periodic array of identical circular cylinders in a homogeneous matrix, and whose dielectric properties are complex-valued. Efficient formulas are provided to determine the effective com ... [J. Math. Phys. 54, 053505 (2013)] published Mon May 6, 2013.

Coulomb problem in non-commutative quantum mechanics

Veronika Galikova and Peter Presnajder
The aim of this paper is to find out how it would be possible for space non-commutativity (NC) to alter the quantum mechanics (QM) solution of the Coulomb problem. The NC parameter lambda is to be regarded as a measure of the non-commutativity setting lambda = 0 which means a return to the standard ... [J. Math. Phys. 54, 052102 (2013)] published Mon May 6, 2013.

Asymptotic behaviour of optimal spectral planar domains with fixed perimeter

Dorin Bucur and Pedro Freitas
We consider the problem of minimizing the kth Dirichlet eigenvalue of planar domains with fixed perimeter and show that, as k goes to infinity, the optimal domain converges to the ball with the same perimeter. We also consider this problem within restricted classes of domains such as n-polygons and ... [J. Math. Phys. 54, 053504 (2013)] published Fri May 3, 2013.

Mathematical structure of unit systems

Masao Kitano
We investigate the mathematical structure of unit systems and the relations between them. Looking over the entire set of unit systems, we can find a mathematical structure that is called preorder(or quasi-order). For some pair of unit systems, there exists a relation of preorder such that one unit s ... [J. Math. Phys. 54, 052901 (2013)] published Fri May 3, 2013.

Schrodinger-Virasoro Lie conformal algebra

Yucai Su and Lamei Yuan
We first construct two new nonsimple conformal algebras associated with the Schrodinger-Virasoro Lie algebra and the extended Schrodinger-Virasoro Lie algebra, respectively. Then we study conformal derivations and free nontrivial rank one conformal modules of these two conformal algebras. Also, we p ... [J. Math. Phys. 54, 053503 (2013)] published Thu May 2, 2013.

Bohr-Sommerfeld quantization condition for Dirac states derived from an Ermakov-type invariant

Karl-Erik Thylwe and Patrick McCabe
It is shown that solutions of the second-order decoupled radial Dirac equations satisfy Ermakov-type invariants. These invariants lead to amplitude-phase-type representations of the radial spinor solutions, with exact relations between their amplitudes and phases. Implications leading to a Bohr-Somm ... [J. Math. Phys. 54, 052301 (2013)] published Thu May 2, 2013.

Hartman effect and dissipative quantum systems

Samyadeb Bhattacharya and Sisir Roy
The dwell time for dissipative quantum system is shown to increase with barrier width. It clearly precludes Hartman effect for dissipative systems. Here calculation has been done for inverted parabolic potential barrier. ... [J. Math. Phys. 54, 052101 (2013)] published Thu May 2, 2013.

Coulomb-distorted plane wave: Partial wave expansion and asymptotic forms

I. Hornyak and A. T. Kruppa
Partial wave expansion of the Coulomb-distorted plane wave is determined and studied. Dominant and sub-dominant asymptotic expansion terms are given and leading order three-dimensional asymptotic form is derived. The generalized hypergeometric function F(a, a; a + l + 1, a l; z) is expressed with t ... [J. Math. Phys. 54, 053502 (2013)] published Wed May 1, 2013.

Stability of n-Lie homomorphisms and Jordan n-Lie homomorphisms on n-Lie algebras

Seong Sik Kim, John Michael Rassias, Yeol Je Cho, and Soo Hawn Kim
The motivation of this paper is to apply the Hypers-Ulam stability problems of some kinds of functional equations to the classes of n-Lie homomorphisms and n-Lie algebras by using the structures of n-Lie homomorphisms and n-Lie algebras. In this paper, the generalized Hyers-Ulam-Rassias stability of ... [J. Math. Phys. 54, 053501 (2013)] published Wed May 1, 2013.

Anisotropic Einstein-aether cosmological models

B. Alhulaimi, A. Coley, and P. Sandin
We investigate a class of spatially anisotropic cosmological models in Einstein-aether theory with a scalar field in which the self-interaction potential depends on the timelike aether vector field through the expansion and shear scalars. We derive the evolution equations in terms of expansion-norma ... [J. Math. Phys. 54, 042503 (2013)] published Tue Apr 30, 2013.

Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two-matrix model

M. Bertola, M. Gekhtman, and J. Szmigielski
We apply the nonlinear steepest descent method to a class of 3 x 3 Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix random model. The general case of two equilibrium measures supported on an arbitrary number of intervals is considered. In this case, we solve the Riemann ... [J. Math. Phys. 54, 043517 (2013)] published Mon Apr 29, 2013.

The constitutive tensor of linear elasticity: Its decompositions, Cauchy relations, null Lagrangians, and wave propagation

Yakov Itin and Friedrich W. Hehl
In linear anisotropic elasticity, the elastic properties of a medium are described by the fourth rank elasticity tensor C. The decomposition of C into a partially symmetric tensor M and a partially antisymmetric tensors N is often used in the literature. An alternative, less well-known decomposition ... [J. Math. Phys. 54, 042903 (2013)] published Mon Apr 29, 2013.

On the Weyl tensor classification in all dimensions and its relation with integrability properties

Carlos Batista
In this paper the Weyl tensor is used to define operators that act on the space of forms. These operators are shown to have interesting properties and are used to classify the Weyl tensor, the well-known Petrov classification emerging as a special case. Particularly, in the Euclidean signature this ... [J. Math. Phys. 54, 042502 (2013)] published Fri Apr 26, 2013.

Recursive procedures for Krall-Sheffer operators

Allan P. Fordy and Michael J. Scott
We consider the Krall-Sheffer class of admissible, partial differential operators in the plane. We concentrate on algebraic structures, such as the role of commuting operators and symmetries. For the polynomial eigenfunctions, we give explicit forms of the 3-level recurrence relations and differenti ... [J. Math. Phys. 54, 043516 (2013)] published Thu Apr 25, 2013.

Local Marchenko-Pastur law at the hard edge of sample covariance matrices

Claudio Cacciapuoti, Anna Maltsev, and Benjamin Schlein
Let X be a N x N matrix whose entries are independent identically distributed complex random variables with mean zero and variance (1/N). We study the asymptotic spectral distribution of the eigenvalues of the covariance matrix XX for N --> [infinity]. We prove that the empirical density of eigenv ... [J. Math. Phys. 54, 043302 (2013)] published Thu Apr 25, 2013.

An area law for the bipartite entanglement of disordered oscillator systems

Bruno Nachtergaele, Robert Sims, and Gunter Stolz
We prove an upper bound proportional to the surface area for the bipartite entanglement of the ground state and thermal states of harmonic oscillator systems with disorder, as measured by the logarithmic negativity. Our assumptions are satisfied for some standard models that are almost surely gaples ... [J. Math. Phys. 54, 042110 (2013)] published Wed Apr 24, 2013.

Full counting statistics of stationary particle beams

J. Kiukas, A. Ruschhaupt, and R. F. Werner
We present a general theoretical framework for treating particle beams as time-stationary limits of many particle systems. Due to stationarity, the total particle number diverges, and a description in Fock space is no longer possible. Nevertheless, we show that when describing the particle detection ... [J. Math. Phys. 54, 042109 (2013)] published Tue Apr 23, 2013.

The Schrodinger operator on an infinite wedge with a tangent magnetic field

Nicolas Popoff
We study a model Schrodinger operator with constant magnetic field on an infinite wedge with Neumann boundary condition. The magnetic field is assumed to be tangent to a face. We compare the bottom of the spectrum to the model spectral quantities coming from the regular case. We are particularly mot ... [J. Math. Phys. 54, 041507 (2013)] published Tue Apr 23, 2013.

Estimates on the eigenvalues of the clamped plate problem on domains in Euclidean spaces

Selma Yıldırım Yolcu and Turkay Yolcu
The purpose of this article is two-fold. First, we obtain some certain bounds for the sums of (positive and negative) powers of the eigenvalues of the clamped plate problem of the Dirichlet bi-Laplacian operator Delta|, restricted to a bounded domain [script D][subset or is implied by][openface R] w ... [J. Math. Phys. 54, 043515 (2013)] published Mon Apr 22, 2013.

Multi-soliton propagation in a generalized inhomogeneous nonlinear Schrodinger-Maxwell-Bloch system with loss/gain driven by an external potential

M. S. Mani Rajan and A. Mahalingam
In this paper, we introduce a system of the nonlinear Schrodinger-Maxwell-Bloch equation with variable coefficients which represents the propagation of optical pulses in an inhomogeneous erbium doped fiber with loss/gain driven by an external potential. The one and two soliton solutions in explicit ... [J. Math. Phys. 54, 043514 (2013)] published Mon Apr 22, 2013.

Partial transpose of random quantum states: Exact formulas and meanders

Motohisa Fukuda and Piotr Sniady
We investigate the asymptotic behavior of the empirical eigenvalues distribution of the partial transpose of a random quantum state. The limiting distribution was previously investigated via Wishart random matrices indirectly (by approximating the matrix of trace 1 by the Wishart matrix of random tr ... [J. Math. Phys. 54, 042202 (2013)] published Mon Apr 22, 2013.

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

B. Opanchuk and P. D. Drummond
We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved ... [J. Math. Phys. 54, 042107 (2013)] published Mon Apr 22, 2013.

Spectral properties of a confined nonlinear quantum oscillator in one and three dimensions

Axel Schulze-Halberg and Christopher R. Gordon
We analyze the spectral behaviour of a nonlinear quantum oscillator model under confinement. The underlying potential is given by a harmonic oscillator interaction plus a nonlinear term that can be weakened or strengthened through a parameter. Numerical eigenvalues of the model in one and three dime ... [J. Math. Phys. 54, 042108 (2013)] published Mon Apr 22, 2013.

Virasoro type algebraic structure hidden in the constrained discrete Kadomtsev-Petviashvili hierarchy

Maohua Li, Chuanzhong Li, Keilei Tian, Jingsong He, and Yi Cheng
In this paper, we construct the additional symmetries of one-component constrained discrete Kadomtsev-Petviashvili hierarchy, and then prove that the algebraic structure of the symmetry flows is the positive half of Virasoro algebra. ... [J. Math. Phys. 54, 043512 (2013)] published Fri Apr 19, 2013.

Tri-Hamiltonian duality between the Wadati-Konno-Ichikawa hierarchy and the Song-Qu-Qiao hierarchy

Kai Tian and Q. P. Liu
A linear eigenvalue problem is constructed for the gradients of the eigenvalue of the Wadati-Konno-Ichikawa (WKI) spectral problem. This in turn leads to a compatible pair of Hamiltonian operators, which endows the WKI hierarchy with a bi-Hamiltonian structure. Furthermore, a proper recombination of ... [J. Math. Phys. 54, 043513 (2013)] published Fri Apr 19, 2013.

Noncommutative Common Cause Principles in algebraic quantum field theory

Gabor Hofer-Szabo and Peter Vecsernyes
States in algebraic quantum field theory typically establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivat ... [J. Math. Phys. 54, 042301 (2013)] published Fri Apr 19, 2013.

Soliton cellular automaton associated with D-crystal B

Kailash C. Misra and Evan A. Wilson
A solvable vertex model in ferromagnetic regime gives rise to a soliton cellular automaton which is a discrete dynamical system in which site variables take on values in a finite set. We study the scattering of a class of soliton cellular automata associated with the U(D)-perfect crystal B. We calcu ... [J. Math. Phys. 54, 043301 (2013)] published Fri Apr 19, 2013.

Elliptic (N, N[prime])-soliton solutions of the lattice Kadomtsev-Petviashvili equation

Sikarin Yoo-Kong and Frank Nijhoff
Elliptic soliton solutions, comprising a soliton-type hierarchy of functions based on an elliptic seed solution, are constructed using elliptic Cauchy matrices, for a family of integrable lattice equations of Kadomtsev-Petviashvili (KP) type. This family consists of the lattice KP, modified KP, and ... [J. Math. Phys. 54, 043511 (2013)] published Thu Apr 18, 2013.