2004/07/16 by J. L. Garcia-Palacios, J L García-Palacios, D. Zueco +1 · 2 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Statistical Mechanics and Entropy #cond-mat.other #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/0305-4470/37/45/003
published as J. Phys. A: Math. Gen. 37 (2004) 10735-10770 · 36 pages, 8 figures. submitted to J. Phys. A: Math. Gen
arxiv created 2004/07/16 · openalex publication_date 2004/10/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
The continued-fraction method of solving classical Fokker–Planck equations has been adapted to tackle quantum master equations of the Caldeira–Leggett type. This was 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 us 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).