Exact results for nonequilibrium dynamics in Wigner phase space

Abstract

We study time evolution of Wigner function of an initially interacting one-dimensional quantum gas following the switch-off of the interactions. For the scenario where at t=0the interactions are suddenly suppressed, we derive a relationship between the dynamical Wigner function and its initial value. A two-particle system initially interacting through two different interactions of Dirac delta type is examined. For a system of particles that is suddenly let to move ballistically (without interactions) in a harmonic trap in d dimensions, and using time evolution of one-body density matrix, we derive a relationship between the time dependent Wigner function and its initial value. Using the inverse Wigner transform we obtain, for an initially harmonically trapped noninteracting particles in ddimensions, the scaling law satisfied by the density matrix at time tafter a sudden change of the trapping frequency. Finally, the effects of interactions are analyzed in the dynamical Wigner function.