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Non-Equilibrium Statistical Mechanics of Strongly Anharmonic Chains of Oscillators

Jean-Pierre Eckmann·Martin Hairer
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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 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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Jean-Pierre Eckmann, Martin Hairer. 1999-09-24. Non-Equilibrium Statistical Mechanics of Strongly Anharmonic Chains of Oscillators. https://doi.org/10.1007/s002200000216

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