Communications in Mathematical Physics

, Volume 212, Issue 1, pp 105–164 | Cite as

Non-Equilibrium Statistical Mechanics¶of Strongly Anharmonic Chains of Oscillators

  • J.-P. Eckmann
  • M. Hairer

Abstract:

We study the model of a strongly non-linear chain of particles coupled to two heat baths at different temperatures. Our main result is the existence and uniqueness of a stationary state at all temperatures. This result extends those of Eckmann, Pillet, Rey-Bellet [EPR99a, EPR99b] to potentials with essentially arbitrary growth at infinity. This extension is possible by introducing a stronger version of Hörmander's theorem for Kolmogorov equations to vector fields with polynomially bounded coefficients on unbounded domains.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • J.-P. Eckmann
    • 1
  • M. Hairer
    • 1
  1. 1.Dépt. de Physique Théorique, Université de Genève, 1211 Genève 4, Switzerland.¶E-mail: Jean-Pierre.Eckmann@physics.unige.ch; Martin.Hairer@physics.unige.chCH
  2. 2.Section de Mathéematiques, Université de Genève, 1211 Genève 4, SwitzerlandCH

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