Approach to equilibrium for a class of random quantum models of infinite range

Abstract

We consider random generalizations of a quantum model of infinite range introduced by Emch and Radin. The generalization allows a neat extension from the class $l_1$ of absolutely summable lattice potentials to the optimal class $l_2$ of square summable potentials first considered by Khanin and Sinai and generalised by van Enter and van Hemmen. The approach to equilibrium in the case of a Gaussian distribution is proved to be faster than for a Bernoulli distribution for both short-range and long-range lattice potentials. While exponential decay to equilibrium is excluded in the nonrandom $l_1$ case, it is proved to occur for both short and long range potentials for Gaussian distributions, and for potentials of class $l_2$ in the Bernoulli case. Open problems are discussed.

10 pages, no figures. This last version, to appear in J. Stat. Phys., corrects some minor errors and includes additional references and comments on the relation to experiments

References in corpus (6)

• Response of non-equilibrium systems at criticality: Ferromagnetic models in dimension two and above
• Universality of algebraic laws in Hamiltonian systems
• Thermodynamics and Universality for Mean Field Quantum Spin Glasses
• Dynamics of a mean spherical model with competing interactions
• Thermodynamic Limit for Finite Dimensional Classical and Quantum Disordered Systems
• Kinetic Theory Approach to the SK Spin Glass Model with Glauber Dynamics

Cited by in corpus (3)

• Diverging equilibration times in long-range quantum spin models
• Universal threshold for the dynamical behavior of lattice systems with long-range interactions
• The ground state energy per site of the quantum and classical Edwards-Anderson spin-glass model in the thermodynamic limit