A systematic derivation of exact generalized Brownian motion theory

Journal of Statistical Physics - 1975
Sture Nordholm1, Robert Zwanzig2
1The James Franck Institute, The University of Chicago, Chicago
2Institute of Fluid Dynamics and Applied Mathematics, The University of Maryland, College Park

Tóm tắt

We present here a simple unified derivation of the exact Fokker-Planck equation obtained earlier by Zwanzig and the exact Langevin and transport equations derived by Mori. The derivation, based on the use of a Hilbert space formulation of the dynamics, leads to substantial generalizations of these results in a straightforward manner. We obtain nonlinear Langevin equations for classical systems and discuss the extension of the theory to driven transport and to quantum dynamics based either on the use of density matrices or Γ-space densities as suggested by Wigner. Remaining limitations of the theory are pointed out.

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Journal of Statistical Physics

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