Time evolution of infinite anharmonic systems

Oscar E. Lanford, Joel L. Lebowitz, Elliott H. Lieb

Research output: Contribution to journalArticle

40 Scopus citations

Abstract

We prove the existence of a time evolution for infinite anharmonic crystals for a large class of initial configurations. When there are strong forces tying particles to their equilibrium positions then the class of permissible initial conditions can be specified explicitly; otherwise it can only be shown to have full measure with respect to the appropriate Gibbs state. Uniqueness of the time evolution is also proven under suitable assumptions on the solutions of the equations of motion.

Original languageEnglish (US)
Pages (from-to)453-461
Number of pages9
JournalJournal of Statistical Physics
Volume16
Issue number6
DOIs
StatePublished - Jun 1 1977

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Existence of time evolution
  • strong restoring forces
  • uniqueness

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    Lanford, O. E., Lebowitz, J. L., & Lieb, E. H. (1977). Time evolution of infinite anharmonic systems. Journal of Statistical Physics, 16(6), 453-461. https://doi.org/10.1007/BF01152283