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

David Guéry-Odelin 1 J. G. Muga 2, 3 M. J. Ruiz-Montero 4 E. Trizac 5

Physical Review Letters, American Physical Society, 2014, 112, pp.180602

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.

  • 1. Atomes Froids (LCAR)
  • 2. Departamento de Qumica-Fsica, UPV-EHU
  • 3. Department of Physics, Shanghai University
  • 4. Fisica Teorica, Universidad de Sevilla
  • 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques