Equilibrium states for interactions with acoustic phonons

The motivation of Iris paper is a result of A. Majorana ([6],[12]) concerni ng the interactions with optical phonons. He proved that there were equilib rium states which were not Maxwellian distributions (or Fermi-Dirac distrib utions in the nonlinear case). Then the diffusion approximation of the nonlinear electron-optical phonon c ollision mechanisms, studied by P.A. Markowich, F, Poupaud and C. Schmeiser in [10], gave a new energy dependent drift-diffusion model. Using this wor k, are are interested in the interactions with acoustic phonons : we prove here that the collision operator thermalizes towards Maxwellian (or Fermi-D irac) distributions. Hence we can predict fluid limits similar to the standard drift-diffusion m odels.