A singular perturbation approach to non-Markovian escape rate problems

Journal Article · Tue Apr 01 04:00:00 EST 1986 · SIAM J. Appl. Math.; (United States)

DOI:https://doi.org/10.1137/0146019· OSTI ID:5727643

Dygas, M M; Matkowsky, B J; Schuss, Z

The authors employ singular perturbation methods to examine the generalized Langevin equation which describes the dynamics of a Brownian particle in an arbitrary potential force field, acted on by a fluctuating force describing collisions between the Brownian particle and lighter particles comprising a thermal bath. In contrast to models in which the collisions occur instantaneously, and the dynamics are modeled by a Langevin stochastic equation, they consider the situation in which the collisions do not occur instantaneously, so that the process is no longer a Markov process and the generalized Langevin equation must be employed. They compute expressions for the mean exit time of the Brownian particle from the potential well in which it is confined.

• Research Organization: Dept. of Engineering Sciences and Applied Mathematics, Technological Inst., Northwestern Univ., Evanston, IL 60201
• DOE Contract Number: AC02-78ER04650
• OSTI ID: 5727643
• Journal Information: SIAM J. Appl. Math.; (United States), Journal Name: SIAM J. Appl. Math.; (United States) Vol. 46:2; ISSN SMJMA
• Country of Publication: United States
• Language: English

Related Subjects

640410* -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BROWNIAN MOVEMENT
COLLISIONS
EQUATIONS
FLUCTUATIONS
LANGEVIN EQUATION
PERTURBATION THEORY
STOCHASTIC PROCESSES
TIME DEPENDENCE
VARIATIONS