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By exploring a phase space hydrodynamics description of one-dimensional freeFermi gas, we discuss how systems settle down to steady states described by thegeneralized Gibbs ensembles through quantum quenches. We investigate timeevolutions of the Fermions which are trapped in external potentials or a circlefor a variety of initial conditions and quench protocols. We analyticallycompute local observables such as particle density and show that they alwaysexhibit power law relaxation at late times. We find a simple rule whichdetermines the power law exponent. Our findings are, in principle, observablein experiments in an one dimensional free Fermi gas or Tonk's gas (Bose gaswith infinite repulsion).

Quantum quench and thermalization of one-dimensional Fermi gas via phase space hydrodynamics