Non-Equilibrium Statistical Mechanics of Strongly Anharmonic Chains of Oscillators

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

1999-09-24

arxiv.org/abs/chao-dyn/9909035v1

Nonlinear Sciences

Chaotic Dynamics

~60 pages, 3 figures

Scientific paper

10.1007/s002200000216

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 H\"ormander's theorem for Kolmogorov equations to vector fields with polynomially bounded coefficients on unbounded domains.

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