Quantum master equation in phase space: Application to the Brownian motion in a periodic potentialW. T. Coffey1, Yu. P. Kalmykov2, S. V. Titov1, 3 and B. P. Mulligan1
1 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
received 14 November 2006; accepted in final form 23 November 2006; published January 2007
published online 15 January 2007
The quantum Brownian motion of a particle in a periodic potential is treated using the master equation for the Wigner distribution function W(x, p, t) in phase space (x, p). Explicit equations for the diffusion coefficients of the master equation for this dissipative quantum system are derived. The dynamic structure factor S(k, t) 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.
03.65.Yz - Decoherence; open systems; quantum statistical methods .
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion .
© Europhysics Letters Association 2007