  The continued-fraction method to solve classical Fokker--Planck equations has
been adapted to tackle quantum master equations of the Caldeira--Leggett type.
This can be done taking advantage of the phase-space (Wigner) representation of
the quantum density matrix. The approach differs from those in which some
continued-fraction expression is found for a certain quantity, in that the full
solution of the master equation is obtained by continued-fraction methods. This
allows to study in detail the effects of the environment (fluctuations and
dissipation) on several classes of nonlinear quantum systems. We apply the
method to the canonical problem of quantum Brownian motion in periodic
potentials both for cosine and ratchet potentials (lacking inversion symmetry).
