Rate description of Fokker-Planck processes with time-dependent parameters
Abstract
The reduction of a continuous Markov process with multiple metastable states to a discrete rate process is investigated in the presence of slow time-dependent parameters such as periodic external forces or slowly fluctuating barrier heights. A quantitative criterion is provided under which condition a kinetic description with time-dependent frozen rates applies and nonadiabatic corrections to the frozen rates are obtained. Finally it is shown how the long-time behavior of the underlying continuous process can be retrieved from the knowledge of the discrete process by means of an appropriate random decoration of the discrete states. As a particular example of the presented theory an overdamped bistable Brownian oscillator with periodic driving is discussed.
- Publication:
-
Physical Review E
- Pub Date:
- April 2004
- DOI:
- 10.1103/PhysRevE.69.046109
- arXiv:
- arXiv:cond-mat/0307498
- Bibcode:
- 2004PhRvE..69d6109T
- Keywords:
-
- 02.50.Ga;
- 82.20.Uv;
- 82.37.-j;
- 82.39.Rt;
- Markov processes;
- Stochastic theories of rate constants;
- Single molecule kinetics;
- Reactions in complex biological systems;
- Condensed Matter - Statistical Mechanics
- E-Print:
- doi:10.1103/PhysRevE.69.046109