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DY: Fachverband Dynamik und Statistische Physik
DY 33: Brownian Motion, Stochastic Processes, Transport I
DY 33.3: Talk
Thursday, March 17, 2011, 14:30–14:45, HÜL 186
Quantum master equation in phase space applied to the Brownian motion in a tilted periodic potential — •William Coffey1, Yuri Kalmykov2, Sergey Titov3, Liam Cleary4, and William Dowling1 — 1Department of Electronic and Electrical Engineering, Trinity College, Dublin 2, Ireland — 2Laboratoire de Mathématiques, Physique et Systèmes, Université de Perpignan, 52, Avenue de Paul Alduy, 66860 Perpignan Cedex, France — 3Institute of Radio Engineering and Electronics, Russian Acad. Sci., Vvedenskii Square 1,Fryazino 141190, Russia — 4Massachusetts Institute of Technology
Quantum effects in the Brownian motion of a particle in a tilted cosine potential are treated in the high temperature and weak bath-particle coupling limit using the semiclassical master equation for the time evolution of the Wigner distribution function in phase space proposed by Coffey et al. [PCCP 9, 3361, 2007]. The differential recurrence relation generated from the quantum master equation by expanding the distribution function in Fourier series are solved using matrix continued fractions yielding both the time-independent and the time-dependent periodic solutions. The time-independent periodic solution is of interest in calculating quantum effects in the dc current-voltage characteristic of a Josephson junction including the capacitance, while the time-dependent periodic solution governs dynamical properties of the junction in the locked state such as the impedance, etc. In the limit of high damping the results reproduce those yielded by the semiclassical Smoluchowski equation [W. Coffey et.al, PRE 78, 031114, 2008].