2009/04/30 by Walter F. Wreszinski
Mathematics · Physics and Astronomy · #Bernoulli's principle #Class (philosophy) #Exponential function #Gaussian #Lattice (music) #Quantum #Random Matrices and Applications #Range (aeronautics) #Square lattice #Statistical Mechanics and Entropy #Stochastic processes and statistical mechanics #cond-mat.dis-nn #math-ph #math.MP #msc:37N20 #msc:82C10
paper · pdf · doi:10.1007/s10955-009-9889-8
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
arxiv created 2009/11/23 · openalex publication_date 2009/12/01 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 l1 of absolutely summable lattice potentials to the optimal class l2 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 l1 case, it is proved to occur for both short and long range potentials for Gaussian distributions, and for potentials of class l2 in the Bernoulli case. Open problems are discussed.