Liouville Ergodicity of Linear Multi-Particle Hamiltonian System with One Marked Particle Velocity Flips
A.A. Lykov, V.A. Malyshev
2015, v.21, Issue 2, 381-412
ABSTRACT
We consider multi-particle systems with linear deterministic hamiltonian
dynamics. Besides Liouville measure it has continuum of invariant
tori and thus continuum of invariant measures. But
if one specified
particle is subjected to a simple linear deterministic transformation
(velocity flip) in random time moments,
we prove convergence to Liouville
measure for any initial state. For the proof it appeared necessary
to study non-linear transformations on the energy surface.
Keywords: non-equilibrium statistical mechanics, convergence to equilibrium, Liouville measure
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