Volume 77, Number 2, January 2007
|Number of page(s)||6|
|Published online||15 January 2007|
Quantum master equation in phase space: Application to the Brownian motion in a periodic potential
Department of Electronic and Electrical Engineering, Trinity College - Dublin 2, Ireland
2 Laboratoire MEPS, Université de Perpignan - 52 Avenue de Paul Alduy, 66860 Perpignan Cedex, France
3 Institute of Radio Engineering and Electronics, Russian Academy of Sciences - Vvedenskii Square 1, Fryazino, 141190, Russia
Accepted: 23 November 2006
The quantum Brownian motion of a particle in a periodic potential is treated using the master equation for the Wigner distribution function in phase space . Explicit equations for the diffusion coefficients of the master equation for this dissipative quantum system are derived. The dynamic structure factor and escape rate are evaluated using matrix continued fractions. The matrix continued fraction calculation for agrees well with the analytical solution of the corresponding quantum Kramers turnover problem.
PACS: 03.65.Yz – Decoherence; open systems; quantum statistical methods / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© Europhysics Letters Association, 2007
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