Kramers equation for a charged Brownian particle: The exact solution
  We report the exact fundamental solution for Kramers equation associated to a brownian gas of charged particles, under the influence of homogeneous (spatially uniform) otherwise arbitrary, external mechanical, electrical and magnetic fields. Some applications are presented, namely the hydrothermodynamical picture for Brownian motion in the long time regime. 
Tania P. Simoes and Roberto E. Lagos