Exact non-equilibrium solutions of the Boltzmann equation under a time-dependent external force
arXiv:1404.0502 · doi:10.1103/PhysRevLett.112.180602
Abstract
We construct a novel class of exact solutions to the Boltzmann equation, in both its classical and quantum formulation, for arbitrary collision laws. When the system is subjected to a specific external forcing, the precise form of which is worked out, non equilibrium damping-less solutions are admissible. They do not contradict the -theorem, but are constructed from its requirements. Interestingly, these solutions hold for time-dependent confinement. We exploit them, in a reverse-engineering perspective, to work out a protocol that shortcuts any adiabatic transformation between two equilibrium states in an arbitrarily short time-span, for an interacting system. Particle simulations of the direct Monte Carlo type fully corroborate the analytical predictions.
arXiv comment5 pages, 1 figure
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