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The generalized Smoluchowski equation and non-Markovian dynamics

1986; American Institute of Physics; Volume: 84; Issue: 10 Linguagem: Inglês

10.1063/1.449892

1520-9032

Shoichi Okuyama, David W. Oxtoby,

Nonlinear Dynamics and Pattern Formation

Starting from the generalized Langevin equation, we derive a generalized Smoluchowski equation. This equation provides a general framework for problems of non-Markovian barrier crossing dynamics. We consider the dynamics of a Brownian particle in a harmonic well and on an inverted harmonic potential, and rederive the Grote–Hynes formula for barrier crossing rate constants in the high viscosity limit. In so doing, we answer some questions about possible limits to the validity of that result at high viscosities.