JMP: Statistical Physics

Proof of rounding by quenched disorder of first order transitions in low-dimensional quantum systems

Michael Aizenman, Rafael L. Greenblatt, and Joel L. Lebowitz
We prove that for quantum lattice systems in d <= 2 dimensions the addition of quenched disorder rounds any first order phase transition in the corresponding conjugate order parameter, both at positive temperatures and at T = 0. For systems with continuous symmetry the statement extends up to d <= 4 ... [J. Math. Phys. 53, 023301 (2012)] published Wed Feb 1, 2012.

Dispersive estimates for harmonic oscillator systems

Vita Borovyk and Robert Sims
We consider a large class of harmonic systems, each defined as a quasi-free dynamics on the Weyl algebra over [script-l]([openface Z]). In contrast to recently obtained, short-time locality estimates, known as Lieb-Robinson bounds, we prove a number of long-time dispersive estimates for these models ... [J. Math. Phys. 53, 013302 (2012)] published Mon Jan 23, 2012.

Circular law and arc law for truncation of random unitary matrix

Zhishan Dong, Tiefeng Jiang, and Danning Li
Let V be the m x m upper-left corner of an n x n Haar-invariant unitary matrix. Let lambda, …, lambda be the eigenvalues of V. We prove that the empirical distribution of a normalization of lambda, …, lambda goes to the circular law, that is, the uniform distribution on {z[is-an-el ... [J. Math. Phys. 53, 013301 (2012)] published Fri Jan 20, 2012.

Specific heat anomalies of small quantum systems subjected to finite baths

Hideo Hasegawa
We have studied the specific heat of the (N + N) model for an N-body harmonic oscillator (HO) system which is strongly coupled to an N-body HO bath without dissipation. The system specific heat of C(T) becomes Nk at T --> [infinity] and vanishes at T = 0 in accordance with the third law of thermodyn ... [J. Math. Phys. 52, 123301 (2011)] published Tue Dec 20, 2011.

Counting spanning trees in self-similar networks by evaluating determinants

Yuan Lin, Bin Wu, Zhongzhi Zhang, and Guanrong Chen
Spanning trees are relevant to various aspects of networks. Generally, the number of spanning trees in a network can be obtained by computing a related determinant of the Laplacian matrix of the network. However, for a large generic network, evaluating the relevant determinant is computationally int ... [J. Math. Phys. 52, 113303 (2011)] published Wed Nov 16, 2011.

Absence of orderings in Hubbard models

Jacek Wojtkiewicz
In this paper, an absence of certain orderings in multiparameter family of Hubbard models is proved. A technical tool is a reflection positivity, which allows to establish upper bounds on certain susceptibilities. These bounds in turn imply an absence of magnetic, charge, and superconducting orderin ... [J. Math. Phys. 52, 113302 (2011)] published Tue Nov 8, 2011.

Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit

Dmitri Finkelshtein, Yuri Kondratiev, Oleksandr Kutoviy, and Eugene Lytvynov
Let Gamma denote the space of all locally finite subsets (configurations) in [openface R]. A stochastic dynamics of binary jumps in continuum is a Markov process on Gamma in which pairs of particles simultaneously hop over [openface R]. We discuss a non-equilibrium dynamics of binary jumps. We prove ... [J. Math. Phys. 52, 113301 (2011)] published Thu Nov 3, 2011.

Weak coupling limits in a stochastic model of heat conduction

Frank Redig and Kiamars Vafayi
We study the Brownian momentum process, a model of heat conduction, weakly coupled to heat baths. In two different settings of weak coupling to the heat baths, we study the non-equilibrium steady state and its proximity to the local equilibrium measure in terms of the strength of coupling. For three ... [J. Math. Phys. 52, 093303 (2011)] published Mon Sep 26, 2011.

Universality for eigenvalue correlations from the unitary ensemble associated with a family of singular weights

Shuai-Xia Xu, Yu-Qiu Zhao, and Jian-Rong Zhou
We study the asymptotic behavior of the eigenvalue correlations for the unitary ensemble associated with a family of singular weights w(x; [mu]) = exp { (1 x)}, x [is-an-element-of] ( 1, 1) for [mu] > 0. When [mu] [is-an-element-of] (0, 1/2) these are Szego class weights, and are non-Szego when [ ... [J. Math. Phys. 52, 093302 (2011)] published Fri Sep 23, 2011.

On the area of excursion sets of spherical Gaussian eigenfunctions

Domenico Marinucci and Igor Wigman
The high frequency behaviour for random eigenfunctions of the spherical Laplacian has been recently the object of considerable interest, also because of strong motivation arising from physics and cosmology. In this paper, we are concerned with the high frequency behaviour of excursion sets; in parti ... [J. Math. Phys. 52, 093301 (2011)] published Fri Sep 2, 2011.

Uniqueness of steady-state solutions for thermodynamically consistent Becker-Doring models

Vincent Ssemaganda, Katharina Holstein, and Gerald Warnecke
Dreyer and Duderstadt [J. Stat. Phys. 123, 1 (2006)] proposed a modification of the standard mass-conserving Becker-Doring model. In this paper we solve for steady-state solutions to two versions of the Becker-Doring model. One is the modified mass-conserving model introduced by Dreyer and Duderstad ... [J. Math. Phys. 52, 083304 (2011)] published Thu Aug 25, 2011.

Diffusive behavior from a quantum master equation

Jeremy Clark, W. De Roeck, and Christian Maes
We study a general class of translation invariant quantum Markov evolutions for a particle on [openface Z]. The evolution consists of free flow, interrupted by scattering events. We assume spatial locality of the scattering events and exponentially fast relaxation of the momentum distribution. It is ... [J. Math. Phys. 52, 083303 (2011)] published Thu Aug 18, 2011.

On form factors of the conjugated field in the nonlinear Schrodinger model

K. K. Kozlowski
Izergin-Korepin's lattice discretization of the nonlinear Schrodinger model along with Oota's inverse problem provides one with determinant representations for the form factors of the lattice discretized conjugated field operator. We prove that these form factors converge, in the zero lattice spacin ... [J. Math. Phys. 52, 083302 (2011)] published Tue Aug 16, 2011.

Exact propagator for a Fokker-Planck equation, first passage time distribution, and anomalous diffusion

A. T. Silva, E. K. Lenzi, L. R. Evangelista, M. K. Lenzi, H. V. Ribeiro et al.
We obtain an exact form for the propagator of the Fokker-Planck equation [partial-derivative]rho = [partial-derivative]([script D](x)[partial-derivative]rho) [partial-derivative](F(x, t)rho), with [script D](x)=[script D]-tilde |x| in presence of the external force F(x,t)=k(t)x+([script K]/x)|x|. Us ... [J. Math. Phys. 52, 083301 (2011)] published Wed Aug 10, 2011.

Phase induced transport of a Brownian particle in a periodic potential in the presence of an external noise: A semiclassical treatment

Satyabrata Bhattacharya, Sudip Chattopadhyay, Pinaki Chaudhury, and Jyotipratim Ray Chaudhuri
We develop, invoking a suitable system-reservoir model, the Langevin equation with a state-dependent dissipation associated with a quantum Brownian particle submerged in a heat bath that offers a state-dependent friction to study the directed motion (by studying the phase-induced current) in the pre ... [J. Math. Phys. 52, 073302 (2011)] published Tue Jul 26, 2011.

A microscopic two-band model for the electron-hole asymmetry in high-T superconductors and reentering behavior

J.-B. Bru, W. de Siqueira Pedra, and A.-S. Domel
To our knowledge there is no rigorously analyzed microscopic model explaining the electron-hole asymmetry of the critical temperature seen in high-T cuprate superconductors at least no model not breaking artificially this symmetry. We present here a microscopic two-band model based on the structure ... [J. Math. Phys. 52, 073301 (2011)] published Mon Jul 11, 2011.

Binary jumps in continuum. I. Equilibrium processes and their scaling limits

Dmitri L. Finkelshtein, Yuri G. Kondratiev, Oleksandr V. Kutoviy, and Eugene Lytvynov
Let Gamma denote the space of all locally finite subsets (configurations) in [openface R]. A stochastic dynamics of binary jumps in continuum is a Markov process on Gamma in which pairs of particles simultaneously hop over [openface R]. In this paper, we study an equilibrium dynamics of binary jumps ... [J. Math. Phys. 52, 063304 (2011)] published Fri Jun 24, 2011.

Spin-spin correlation functions of the q-valence-bond-solid state of an integer spin model

Chikashi Arita and Kohei Motegi
We consider the valence-bond-solid ground state of the q-deformed higher-spin Affleck, Kennedy, Lieb, and Tasaki model (q-VBS state) with q real. We investigate the eigenvalues and eigenvectors of a matrix (G matrix), which is constructed from the matrix product representation of the q-VBS state. We ... [J. Math. Phys. 52, 063303 (2011)] published Wed Jun 22, 2011.

A counterexample against the Lesche stability of a generic entropy functional

A. El Kaabouchi, C. J. Ou, J. C. Chen, G. Z. Su, and Q. A. Wang
We provide a counterexample to show that the generic form of entropy S(p)=[summation]g(p), is not always stable against small variation of probability distribution (Lesche stability) even if g is concave function on [0, 1] and of class [script C] on ]0, 1]. Our conclusion is that the stability of su ... [J. Math. Phys. 52, 063302 (2011)] published Mon Jun 13, 2011.

Kinetic equations for classical and quantum Brownian particles and eigenfunction expansions as generalized functions

Kazuki Kanki, Satoshi Tanaka, and Tomio Petrosky
We study momentum relaxation processes of a classical and a quantum Brownian particle by considering the eigenvalue problem of the collision operators in the kinetic equations. The collision operators are anti-Hermitian with an appropriate inner product defined by an integral with a weight factor gi ... [J. Math. Phys. 52, 063301 (2011)] published Mon Jun 13, 2011.

Large deviations of the current in stochastic collisional dynamics

Raphael Lefevere, Mauro Mariani, and Lorenzo Zambotti
We consider a class of deterministic local collisional dynamics, showing how to approximate them by means of stochastic models and then studying the fluctuations of the current of energy. We show first that the variance of the time-integrated current is finite and related to the conductivity by the ... [J. Math. Phys. 52, 033302 (2011)] published Fri Mar 18, 2011.