Exponential return to equilibrium for hypoelliptic quadratic systems

M. Ottobre, G. A. Pavliotis, K. Pravda-Starov

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

We study the problem of convergence to equilibrium for evolution equations associated to general quadratic operators. Quadratic operators are non-selfadjoint differential operators with complex-valued quadratic symbols. Under appropriate assumptions, a complete description of the spectrum of such operators is given and the exponential return to equilibrium with sharp estimates on the rate of convergence is proven. Some applications to the study of chains of oscillators and to the generalized Langevin equation are given. (C) 2012 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)4000-4039
Number of pages40
JournalJournal of Functional Analysis
Volume262
Issue number9
DOIs
Publication statusPublished - 1 May 2012

Keywords

  • Quadratic operators
  • Hypoellipticity
  • Return to equilibrium
  • Rate of convergence
  • Chains of oscillators
  • Generalized Langevin equation
  • FOKKER-PLANCK EQUATION
  • NONEQUILIBRIUM STATISTICAL-MECHANICS
  • DIFFERENTIAL-OPERATORS
  • ANHARMONIC CHAINS
  • BEHAVIOR

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