A random matrix model of relaxation

J. L. Lebowitz, L. Pastur

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

We consider a two-level system, S2, coupled to a general n level system, Sn, via a random matrix. We derive an integral representation for the mean reduced density matrix p(t) of S2 in the limit n → ∞, and we identify a model of Sn which possesses some of the properties expected for macroscopic thermal reservoirs. In particular, it yields the Gibbs form for ρ (∞). We also consider an analog of the van Hove limit and obtain a master equation (Markov dynamics) for the evolution of ρ(t) on an appropriate time scale.

Original languageEnglish (US)
Pages (from-to)1517-1534
Number of pages18
JournalJournal of Physics A: Mathematical and General
Volume37
Issue number5
DOIs
StatePublished - Feb 6 2004

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

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