Exact generalized Fokker-Planck equation for arbitrary dissipative quantum systems

Hermann Haken

V. G. Morozov

Nicola Cufaro Petroni, S. De Martino, Silvio De Siena

Shesheng Zhang, Eli Pollak

A study is provided of dynamics and dissipative tunneling in a symmetric quartic double well potential. The numerical solution for the position autocorrelation function obtained through the Wigner–Fokker–Planck equation is compared with numerically exact results of Stockburger and Mak [J. Chem. Phys. 110, 4983 (1999)]. We find that the Wigner–Fokker–Planck dynamics agree well with the numerically exact computations, they account for both quantum coherences as well as quantum tunneling phenomena. This, in contrast to the mixed quantum classical approximation, which does not perform as well.

Victor A. Mikhailov, Nikolay V. Troshkin, Anton M. Trunin

The relaxation of a pair of dipole-dipole interacting two-level atoms with parallel dipole moments in a large dissipative system is studied on the basis of the generalized coherent states method. The Fokker-Planck equation and its exact solution are obtained. Explicit formulas for two-time correlation functions are given. The influence of the magnitude of the interaction on the shape of the radiation line is investigated.

YiJing Yan

We develop a generalized quantum Fokker-Planck theory in a non-Gaussian-Markovian model bath. The semiclassical bath adopted in this work is charactered by three parameters. One denotes the strength of system-bath coupling and the other two are chosen to interpolate smoothly the solvation dynamics between the long- and short-time regimes. The fluctuation-dissipation relation in this model bath is analyzed in detail. Based on this model bath, we derive two sets of coupled Fokker-Planck equations. These two equation sets are equivalent in the second order of system-bath coupling but different in the higher orders. The corresponding reduced Liouville equation in one set of the Fokker-Planck formulation is characterized by a memory relaxation kernel, while that in the other is by a local-time relaxation tensor. Each resulting set of Fokker-Planck equations involves only the reduced density operator and a series of well-characterized Hilbert-space relaxation operators. The present theory is valid for arbitrary time-dependent Hamiltonians and is applicable to the study of quantum coherence and relaxation in various dynamic systems.