Quantum friction in phase space

In this paper we shall study the problem of quantum friction in the Wigner representation. For quadratic Hamiltonians the Wigner equation coincides with the classical Liouville equation although there are distribution functions which depend on the Planck constant. For these distributions the product of the standard deviations of p and q is greater or equal to h/2π so that the uncertainty principle of Heisenberg holds. (orig.)