Caldeira--Leggett quantum master equation in Wigner phase space: continued-fraction solution and application to Brownian motion in periodic potentials
arXiv:cond-mat/0407454 · doi:10.1088/0305-4470/37/45/003
Abstract
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).
36 pages, 8 figures. submitted to J. Phys. A: Math. Gen
References in corpus (18)
- Brownian motors: noisy transport far from equilibrium
- Decoherence, Chaos, and the Second Law
- Wannier-Stark resonances in optical and semiconductor superlattices
- Floquet-Markov description of the parametrically driven, dissipative harmonic quantum oscillator
- Exact time evolution and master equations for the damped harmonic oscillator
- Generalized Uncertainty Relations and Long Time Limits for Quantum Brownian Motion Models
- Demon-free quantum Brownian motors
- Quantum Dissipation versus Classical Dissipation for Generalized Brownian Motion
- Multi-band quantum ratchets
- Phase Space Representation for Open Quantum Systems within the Lindblad Theory
- Quantum Brownian motion in ratchet potentials
- Decoherence in a classically chaotic quantum system: entropy production and quantum--classical correspondence
- Hydrodynamical quantum state reconstruction
- Solving quantum master equations in phase space by continued-fraction methods
- Phase space dynamics of overdamped quantum systems
- Continued Fraction as a Discrete Nonlinear Transform
- Dynamics of Dissipative Quantum Systems--from Path Integrals to Master Equations
- A quantum statistical mechanics model of a three dimensional linear rigid rotator in a bath of oscillators: IV - steady state dielectric properties induced by a. c. and d. c. field coupling
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- Physics at the FQMT'04 conference
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