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

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

2009-04-14

arxiv.org/abs/0904.2130v4

Physics

Mathematical Physics

10 pages, no figures. This last version, to appear in J. Stat. Phys., corrects some minor errors and includes additional refer

Scientific paper

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.

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