LINEAR, NONLINEAR, AND TIME-DEPENDENT RESPONSE OF A DISSIPATIVE QUANTUM PARTICLE IN PERIODIC COSINE POTENTIALS
Yong-Cong Chen · International Journal of Modern Physics B · 1993
We review some of our recent results on the dynamics of a dissipative quantum particle in periodic cosine potentials. The dissipation is modeled by the Caldeira-Leggett prescription. Exact real-time Wigner distributions for the particle alone can be obtained in powers of V0 (the strength of the cosine potentials), which is suitable for calculations of various time-dependent averages. Special interest is devoted to summing over the whole series. For Ohmic dissipation, we have the following results: (a) The Kubo-Einstein relation for the linear response is shown to hold rigorously to all orders. (b) In the small viscosity limit, nearly exact analytic expressions for the nonlinear mobility and the nonlinear time-dependent response are found. (c) The resummation can also be performed in certain regimes of the dissipative Hafstadter problem in two dimensions. These results we believe can have useful applications in experiments in Josephson junctions and other mesoscopic systems.