  Employing time-dependent projection formalism, a Fokker-Planck equation with
non-Markovian transport coefficients is derived for large amplitude collective
motion. Properties of transport coefficients for diffusion processes in a
potential well and along a potential barrier are discussed, and their
connection with the fluctuation-dissipation theorem is investigated. In the
case of diffusion in a potential well, the formalism naturally leads to the
generalization of the well known Einstein relation by including quantum
fluctuations in addition to thermal fluctuations. Furthermore, it is shown that
at low temperatures diffusion along potential barrier is significantly modified
by quantum fluctuations. Explicit expressions for transport coefficients are
presented for the case of the Caldeira-Leggett model.
