  By exploring a phase space hydrodynamics description of one-dimensional free
Fermi gas, we discuss how systems settle down to steady states described by the
generalized Gibbs ensembles through quantum quenches. We investigate time
evolutions of the Fermions which are trapped in external potentials or a circle
for a variety of initial conditions and quench protocols. We analytically
compute local observables such as particle density and show that they always
exhibit power law relaxation at late times. We find a simple rule which
determines the power law exponent. Our findings are, in principle, observable
in experiments in an one dimensional free Fermi gas or Tonk's gas (Bose gas
with infinite repulsion).
