Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
The Journal of Chemical Physics
92 (1990), S. 2526-2535
ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
A time-local Fokker–Planck equation (TLFPE) is derived which accounts for memory effects in stochastic problems. This is expected to provide a computationally efficient method of modeling the phase space evolution of such systems by simple (local time) Langevin equations with Markovian fluctuating forces that are characterized by time-dependent moments; it is this explicit time dependence that describes the memory effects. The TLFPE is derived from the probability theory of non-Markovian systems as a generalization of Chandrasekar's derivation of the Fokker–Planck equation (FPE) from the Chapman–Kolmogarov equation for Markovian systems. In this article it is applied to free particle diffusion and barrier crossing problems, and is shown to give rise to physically realistic results. Further, the form of the TLFPE suggests that the conditions required for systems to exhibit Markovian behavior are less restrictive than the Brownian criterion of separation of time scales between the fluctuating forces and the momentum response of the system. Rather, a sufficient condition is that the time-dependent moments of the TLFPE reach plateau values before the time scale of the phenomenon of interest.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.457944
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