  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 $t=0$ the 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 $d$ dimensions, the scaling law satisfied by the
density matrix at time $t$ after a sudden change of the trapping frequency.
Finally, the effects of interactions are analyzed in the dynamical Wigner
function.
