Europhys. Lett.
Volume 65, Number 6, March 2004
Page(s) 735 - 741
Section General
Published online 01 March 2004
Europhys. Lett., 65 (6) , pp. 735-741 (2004)
DOI: 10.1209/epl/i2003-10134-y

Solving quantum master equations in phase space by continued-fraction methods

J. L. García-Palacios

Departamento de Física de la Materia Condensada e Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza - E-50009 Zaragoza, Spain

(Received 6 October 2003; accepted in final form 28 January 2004)

Inspired by the continued-fraction technique to solve the classical Fokker-Planck equation, we develop continued-fraction methods to solve quantum master equations in phase space (Wigner representation of the density matrix). The approach allows to study several classes of nonlinear quantum systems subjected to environmental effects (fluctuations and dissipation), with the only limitations that the starting master equations may have. We illustrate the method with the canonical problem of quantum Brownian motion in periodic potentials.

03.65.Yz - Decoherence; open systems; quantum statistical methods.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
05.60.-k - Transport processes.

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