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The continued-fraction method to solve classical Fokker--Planck equations hasbeen adapted to tackle quantum master equations of the Caldeira--Leggett type.This can be done taking advantage of the phase-space (Wigner) representation ofthe quantum density matrix. The approach differs from those in which somecontinued-fraction expression is found for a certain quantity, in that the fullsolution of the master equation is obtained by continued-fraction methods. Thisallows to study in detail the effects of the environment (fluctuations anddissipation) on several classes of nonlinear quantum systems. We apply themethod to the canonical problem of quantum Brownian motion in periodicpotentials both for cosine and ratchet potentials (lacking inversion symmetry).Comment: 36 pages, 8 figures. submitted to J. Phys. A: Math. Ge

journal of physics. a, mathematical and general/journal of physics. a, mathematical and general

The Caldeira–Leggett quantum master equation in Wigner phase space: continued-fraction solution and application to Brownian motion in periodic potentials