Hydrodynamics for quasi-free quantum systems
  We consider quasi-free quantum systems and we derive the Euler equation using the so-called hydrodynamic limit. We use Wigner's well-known distribution function and discuss an extension to band distribution functions for particles in a periodic potential. We investigate the Bosonic system of hard rods and calculate fluctuations of the density.   Keywords: Euler equation, quantum distribution function, hydrodynamic limit 
Christian Maes and Wolfgang Spitzer