Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-07-16
J. Phys. A: Math. Gen. 37 (2004) 10735-10770
Physics
Condensed Matter
Statistical Mechanics
36 pages, 8 figures. submitted to J. Phys. A: Math. Gen
Scientific paper
10.1088/0305-4470/37/45/003
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).
Garcia-Palacios J. L.
Zueco David
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