Journal of Mathematical Physics: All Topics

Bi-Hamiltonian structures for integrable systems on regular time scales

Blazej M. Szablikowski, Maciej Blaszak, and Burcu Silindir
A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of delta-pseudodifferential operators, valid on an arbitrary regular time scale, is introduced. The linear Poisson tensors and the related Hamiltonians are d ... [J. Math. Phys. 50, 073502 (2009)] published Thu Jul 2, 2009.

Hill's equation with random forcing parameters: The limit of delta function barriers

Fred C. Adams and Anthony M. Bloch
This paper considers random Hill's equations in the limit where the periodic forcing function becomes a Dirac delta function. For this class of equations, the forcing strength q, the oscillation frequency lambda, and the period (Deltatau) are allowed to vary from cycle to cycle. Such equations arise ... [J. Math. Phys. 50, 073501 (2009)] published Thu Jul 2, 2009.

Quasiperiodic solutions for the cubic complex GinzburgLandau equation

Hongzi Cong, Jianjun Liu, and Xiaoping Yuan
The existence of two-dimensional KolmogorovArnoldMoser invariant tori is proved for cubic complex GinzburgLandau equation of higher spatial dimension. As a consequence, the equation possesses a Cantorian branch of nontraveling-wave quasiperiodic solutions of two-dimensional frequency vector. ... [J. Math. Phys. 50, 063516 (2009)] published Tue Jun 30, 2009.

On the evolution of the cellular automaton of rule 150 from some simple initial states

A. J. Macfarlane
The evolution E in discrete time t of the cellular automaton CA150 of Wolfram rule 150 is studied for certain initial states psi. The values of the cell variables in any state psi considered are all zero outside a principal sequence (PS) of length k within which they take on values 1aa[centered elli ... [J. Math. Phys. 50, 062702 (2009)] published Tue Jun 30, 2009.

Bulk asymptotics of skew-orthogonal polynomials for quartic double well potential and universality in the matrix model

Saugata Ghosh
We derive bulk asymptotics of skew-orthogonal polynomials pi, beta=1, 4, defined with respect to the weight exp(2NV(x)), V(x)=gx/4+tx/2, g>0 and t<0. We assume that as m,N-->[infinity], there exists an epsilon>0 such that epsilon<=(m/N)<=lambdaepsilon, where lambda is the critical value that separat ... [J. Math. Phys. 50, 063515 (2009)] published Fri Jun 26, 2009.

Quantum error correction on infinite-dimensional Hilbert spaces

Cedric Beny, Achim Kempf, and David W. Kribs
We present a generalization of quantum error correction to infinite-dimensional Hilbert spaces. We find that, under relatively mild conditions, much of the structure known from systems in finite-dimensional Hilbert spaces carries straightforwardly over to infinite dimensions. We also find that, at l ... [J. Math. Phys. 50, 062108 (2009)] published Fri Jun 26, 2009.

Flat BogomolnyiPrasadSommerfeld domain walls on two-dimensional KahlerRicci soliton

Bobby Eka Gunara and Freddy Permana Zen
In this paper we address several aspects of flat BogomolnyiPrasadSommerfeld (BPS) domain walls together with their Lorentz invariant vacua of four-dimensional N=1 supergravity coupled to a chiral multiplet. The scalar field spans a one-parameter family of two-dimensional Kahler manifolds satisfying ... [J. Math. Phys. 50, 063514 (2009)] published Thu Jun 25, 2009.

Variational principle for the WheelerFeynman electrodynamics

Jayme De Luca
We adapt the formally defined Fokker action into a variational principle for the electromagnetic-two-body problem. We introduce properly defined boundary conditions to construct a functional of a finite orbital segment into the reals. The boundary conditions for the variational principle are an end ... [J. Math. Phys. 50, 062701 (2009)] published Thu Jun 25, 2009.

On the eigenvalues of the twisted Dirac operator

Marcos Jardim and Rafael F. Leao
Given a compact Riemannian spin manifold whose untwisted Dirac operator has trivial kernel, we find a family of connections [del] for t[is-an-element-of][0,1] on a trivial vector bundle of rank no larger than dim M+1, such that the first eigenvalue of the twisted Dirac operator D is nonzero for t[no ... [J. Math. Phys. 50, 063513 (2009)] published Wed Jun 24, 2009.

An inverse problem for a heat equation with piecewise-constant thermal conductivity

N. S. Hoang and A. G. Ramm
The governing equation is u=(a(x)u), 0<=x<=1, t>0, u(x,0)=0, u(0,t)=0, a(1)u(1,t)=f(t). The extra data are u(1,t)=g(t). It is assumed that a(x) is a piecewise-constant function and f[not identical with]0. It is proved that the function a(x) is uniquely defined by the above data. No restrictions on t ... [J. Math. Phys. 50, 063512 (2009)] published Wed Jun 24, 2009.

Publisher's Note: Influences of degree inhomogeneity on average path length and random walks in disassortative scale-free networks [J. Math. Phys. 50, 033514 (2009)]

Zhongzhi Zhang, Yichao Zhang, Shuigeng Zhou, Ming Yin, and Jihong Guan
Abstract not available. [J. Math. Phys. 50, 069902 (2009)] published Tue Jun 23, 2009.

Erratum: Existence and asymptotic stability for the semilinear wave equation with boundary damping and source term [J. Math. Phys. 49, 053511 (2008)]

Jong Yeoul Park and Tae Gab Ha
Abstract not available. [J. Math. Phys. 50, 069901 (2009)] published Tue Jun 23, 2009.

Inverse momentum expectation values for hydrogenic systems

R. Delbourgo and D. Elliott
By using the Fourier transforms of the general hydrogenic bound state wave functions (as ultraspherical polynomials), one may find expectation values of arbitrary functions of momentum p. In this manner the effect of a reciprocity perturbation b/p can be evaluated for all hydrogenic states. ... [J. Math. Phys. 50, 062107 (2009)] published Tue Jun 23, 2009.

Brownian motion in RobertsonWalker spacetimes from electromagnetic vacuum fluctuations

Carlos H. G. Bessa, V. B. Bezerra, and L. H. Ford
We consider the effects of the vacuum fluctuations of a quantized electromagnetic field on particles in an expanding universe. We find that these particles typically undergo Brownian motion and acquire a nonzero mean squared velocity that depends on the scale factor of the universe. This Brownian mo ... [J. Math. Phys. 50, 062501 (2009)] published Mon Jun 22, 2009.

Applications of automata and graphs: Labeling operators in Hilbert space. II.

Ilwoo Cho and Palle E. T. Jorgensen
We introduced a family of infinite graphs directly associated with a class of von Neumann automaton model [script A]. These are finite state models used in symbolic dynamics: stimuli models and in control theory. In the context of groupoid von Neumann algebras, and an associated fractal group, we pr ... [J. Math. Phys. 50, 063511 (2009)] published Fri Jun 19, 2009.

Mean energy of some interacting bosonic systems derived by virtue of the generalized HellmannFeynman theorem

Hong-yi Fan and Xue-xiang Xu
By virtue of the generalized HellmannFeynman theorem [H. Y. Fan and B. Z. Chen, Phys. Lett. A 203, 95 (1995)], we derive the mean energy of some interacting bosonic systems for some Hamiltonian models without proceeding with diagonalizing the Hamiltonians. Our work extends the field of applications ... [J. Math. Phys. 50, 063303 (2009)] published Fri Jun 19, 2009.

Cones of positive maps and their duality relations

Lukasz Skowronek, Erling Stormer, and Karol Zyczkowski
The structure of cones of positive and k-positive maps acting on a finite-dimensional Hilbert space is investigated. Special emphasis is given to their duality relations to the sets of superpositive and k-superpositive maps. We characterize k-positive and k-superpositive maps with regard to their pr ... [J. Math. Phys. 50, 062106 (2009)] published Fri Jun 19, 2009.

Electromagnetic fields produced by moving sources in a curved beam pipe

Shin-itiro Goto and Robin W Tucker
A new geometrical perturbation scheme is developed in order to calculate the electromagnetic fields produced by charged sources in prescribed motion moving in a nonstraight perfectly conducting beam pipe. The pipe is regarded as a perturbed infinitely long hollow right-circular cylinder. The perturb ... [J. Math. Phys. 50, 063510 (2009)] published Thu Jun 18, 2009.

Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property

Claudio Dappiaggi, Valter Moretti, and Nicola Pinamonti
In a recent paper, we proved that a large class of spacetimes, not necessarily homogeneous or isotropous and relevant at a cosmological level, possesses a preferred codimension 1 submanifold, i.e., the past cosmological horizon, on which it is possible to encode the information of a scalar field the ... [J. Math. Phys. 50, 062304 (2009)] published Thu Jun 18, 2009.

The entries of circular orthogonal ensembles

Tiefeng Jiang
Let V=(v) be a circular orthogonal ensemble. In this paper, for 1<=m<=o(sqrt(n)/log n), we give a bound for the tail probability of max|v(1/n)yy|, where Y=(y,…,y) is a certain n x n matrix whose entries are independent and identically distributed random variables with the standard complex nor ... [J. Math. Phys. 50, 063302 (2009)] published Wed Jun 17, 2009.

On the use of group theoretical and graphical techniques toward the solution of the general N-body problem

W. B. Laing, M. Dunn, and D. K. Watson
Group theoretic and graphical techniques are used to derive the N-body wave function for a system of identical bosons with general interactions through first-order in a perturbation approach. This method is based on the maximal symmetry present at lowest order in a perturbation series in inverse spa ... [J. Math. Phys. 50, 062105 (2009)] published Wed Jun 17, 2009.

Three-dimensional IvanovPetrova manifolds

Giovanni Calvaruso
We introduce a system of partial differential equations, whose solutions determine some large families of three-dimensional IvanovPetrova manifolds, both Riemannian and Lorentzian, in terms of explicit metrics on an open subset of [openface R]. ... [J. Math. Phys. 50, 063509 (2009)] published Wed Jun 17, 2009.

Entanglement and quantum groups

J. K. Korbicz, J. Wehr, and M. Lewenstein
We describe quantum mechanical entanglement in terms of compact quantum groups. We prove an analog of positivity of partial transpose criterion and formulate a Horodecki-type theorem. ... [J. Math. Phys. 50, 062104 (2009)] published Wed Jun 17, 2009.

Solution of the fractional Langevin equation and the MittagLeffler functions

R. Figueiredo Camargo, Ary O. Chiacchio, R. Charnet, and E. Capelas de Oliveira
We introduce the fractional generalized Langevin equation in the absence of a deterministic field, with two deterministic conditions for a particle with unitary mass, i.e., an initial condition and an initial velocity are considered. For a particular correlation function, that characterizes the phys ... [J. Math. Phys. 50, 063507 (2009)] published Tue Jun 16, 2009.

On the imaginary-real ratio rule of power spectra

Min-Ping Qian and Jian-Sheng Xie
The power spectra of real observables for continuous-time systems driven by L-exponential ergodic stationary Markov processes are investigated. We find the necessary and sufficient condition for the power spectra to be monotonic/nonmonotonic, which includes the famous imaginary-real ratio rule as a ... [J. Math. Phys. 50, 063301 (2009)] published Tue Jun 16, 2009.

Hopf algebras for ternary algebras

M. Goze and M. Rausch de Traubenberg
We construct a universal enveloping algebra associated with the ternary extension of Lie (super)algebras called Lie algebra of order three. A PoincareBirkhoffWitt theorem is proven is this context. It this then shown that this universal enveloping algebra can be endowed with a structure of Hopf alge ... [J. Math. Phys. 50, 063508 (2009)] published Tue Jun 16, 2009.

On the infimum of the energy-momentum spectrum of a homogeneous Bose gas

H. D. Cornean, J. Derezinski, and P. Zin
We consider second-quantized homogeneous Bose gas in a large cubic box with periodic boundary conditions at zero temperature. We discuss the energy-momentum spectrum of the Bose gas and its physical significance. We review various rigorous and heuristic results as well as open conjectures about its ... [J. Math. Phys. 50, 062103 (2009)] published Tue Jun 16, 2009.

Light-cone matrix product

M. B. Hastings
We show how to combine the light-cone and matrix product algorithms to simulate quantum systems far from equilibrium for long times. For the case of the XXZ spin chain at Delta=0.5, we simulate to a time of [approximate]22.5. While part of the long simulation time is due to the use of the light-cone ... [J. Math. Phys. 50, 095207 (2009)] published Thu Jun 11, 2009.

Completeness of a fermionic basis in the homogeneous XXZ model

H. Boos, M. Jimbo, T. Miwa, and F. Smirnov
With the aid of the creation operators introduced in our previous works, we show how to construct a basis of the space of quasilocal operators for the homogeneous XXZ chain. ... [J. Math. Phys. 50, 095206 (2009)] published Thu Jun 11, 2009.

Fine structure of the asymptotic expansion of cyclic integrals

K. K. Kozlowski
The asymptotic expansion of n-dimensional cyclic integrals was expressed as a series of functionals acting on the symmetric function involved in the cyclic integral. In this article, we give an explicit formula for the action of these functionals on a specific class of symmetric functions. These res ... [J. Math. Phys. 50, 095205 (2009)] published Thu Jun 11, 2009.

Symmetries and reduction techniques for dissipative models

Marianna Ruggieri and Antonino Valenti
Symmetries and reduction techniques are applied to a mathematical model describing one-dimensional motions in nonlinear dissipative media. Reduced equations through the optimal system of subalgebras are performed and some exact invariant solutions are shown in a physical application. ... [J. Math. Phys. 50, 063506 (2009)] published Thu Jun 11, 2009.

Minimum-error quantum distinguishability bounds from matrix monotone functions: A comment on Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized HolevoCurlander bounds [J. Math. Phys. 50, 032106 (2009)]

Jon Tyson
Matrix monotonicity is used to obtain upper bounds on minimum-error distinguishability of arbitrary ensembles of mixed quantum states. This generalizes one direction of a two-sided bound recently obtained by the author [J. Tyson, J. Math. Phys. 50, 032106 (2009)]. It is shown that the previously obt ... [J. Math. Phys. 50, 062102 (2009)] published Thu Jun 11, 2009.

On the relationship between nonlinear equations integrable by the method of characteristics and equations associated with commuting vector fields

A. I. Zenchuk
It was shown recently that Frobenius reduction of the matrix fields reveals interesting relations among the nonlinear partial differential equations (PDEs) integrable by the inverse spectral transform method (S-integrable PDEs), linearizable by the HopfCole substitution (C-integrable PDEs), and inte ... [J. Math. Phys. 50, 063505 (2009)] published Wed Jun 10, 2009.

Symmetry reduction of quasi-free states

C. G. Torre
Given a group-invariant quasi-free state on the algebra of canonical commutation relations (CCR), we show how group averaging techniques can be used to obtain a symmetry-reduced CCR algebra and reduced quasi-free state. When the group is compact, this method of symmetry reduction leads to standard r ... [J. Math. Phys. 50, 062303 (2009)] published Wed Jun 10, 2009.

Nontrivial systems and the necessity of the scalar quantum mechanics axioms

Jan Kotulek
We discuss the necessity of the axioms of scalar quantum mechanics introduced by Paschke and clearly demonstrate their geometric and/or physical meaning. We show that reasonable nonrelativistic quantum mechanics is exactly specified by the axioms. A system describing the electric AharonovBohm effect ... [J. Math. Phys. 50, 062101 (2009)] published Tue Jun 9, 2009.

Total current fluctuations in the asymmetric simple exclusion process

Craig A. Tracy and Harold Widom
A limit theorem for the total current in the asymmetric simple exclusion process (ASEP) with step initial condition is proven. This extends the result of Johansson on TASEP to ASEP. ... [J. Math. Phys. 50, 095204 (2009)] published Mon Jun 8, 2009.

Gap probabilities in non-Hermitian random matrix theory

G. Akemann, M. J. Phillips, and L. Shifrin
We compute the gap probability that a circle of radius r around the origin contains exactly k complex eigenvalues. Four different ensembles of random matrices are considered: the Ginibre ensembles and their chiral complex counterparts, with both complex (beta=2) or quaternion real (beta=4) matrix el ... [J. Math. Phys. 50, 063504 (2009)] published Mon Jun 8, 2009.

A set of sums for continuous dual q-Hahn polynomials

R. M. Gade
An infinite set {tau(y;r,z)} of linear sums of continuous dual q-Hahn polynomials with prefactors depending on a complex parameter z is studied. The sums tau(y;r,z) have an interpretation in context with tensor product representations of the quantum affine algebra U(sl-hat(2)) involving both a posit ... [J. Math. Phys. 50, 063503 (2009)] published Mon Jun 8, 2009.

The covariant and on-shell statistics in kappa-deformed space-time

Rong-Xin Miao
It has been a long-standing issue to construct the statistics of identical particles in kappa-deformed space-time. In this letter, we investigate different ideas on this problem. Following the ideas of Young and Zegers, we obtain the covariant and on shell kappa two-particle state in 1+1 D in a sim ... [J. Math. Phys. 50, 063502 (2009)] published Thu Jun 4, 2009.

String field theory-inspired algebraic structures in gauge theories

Anton M. Zeitlin
We consider gauge theories in a string field theory-inspired formalism. The constructed algebraic operations lead, in particular, to homotopy algebras of the related Batalin-Vilkovisky theories. We discuss an invariant description of the gauge fixing procedure and special algebraic features of gauge ... [J. Math. Phys. 50, 063501 (2009)] published Thu Jun 4, 2009.

On the spectral analysis of quantum electrodynamics with spatial cutoffs. I.

Toshimitsu Takaesu
In this paper, we consider the spectrum of a model in quantum electrodynamics with a spatial cutoff. It is proven that (1) the Hamiltonian is self-adjoint; (2) under the infrared regularity condition, the Hamiltonian has a unique ground state for sufficiently small values of coupling constants. The ... [J. Math. Phys. 50, 062302 (2009)] published Thu Jun 4, 2009.