Exact non-equilibrium solutions of the Boltzmann equation under a time-dependent external force

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 $H$-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.

5 pages, 1 figure

References in corpus (4)

• Shortcut to adiabaticity for an interacting Bose-Einstein condensate
• Fast optimal transition between two equilibrium states
• Transient energy excitation in shortcuts to adiabaticity for the time dependent harmonic oscillator
• Optimal transport of ultracold atoms in the non-adiabatic regime

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