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

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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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Authors and Affiliations

  1. Dépt. de Physique Théorique, Université de Genève, 1211 Genève 4, Switzerland.¶E-mail: Jean-Pierre.Eckmann@physics.unige.ch; Martin.Hairer@physics.unige.ch, , , , , , CH

    J.-P. Eckmann & M. Hairer

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  1. J.-P. Eckmann
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  2. M. Hairer
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Received: 27 September 1999 / Accepted: 11 January 2000

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Eckmann, JP., Hairer, M. Non-Equilibrium Statistical Mechanics¶of Strongly Anharmonic Chains of Oscillators. Comm Math Phys 212, 105–164 (2000). https://doi.org/10.1007/s002200000216

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  • DOI: https://doi.org/10.1007/s002200000216

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