Exact transformation of a Langevin equation to a fluctuating response equation

Details Exact transformation of a Langevin equation to a fluctuating response equation Exact transformation of a Langevin equation to a fluctuating response equation

2005-01-17

arxiv.org/abs/cond-mat/0501371v3

Physics

Condensed Matter

Statistical Mechanics

14 pages, to appear in J. Phys. A: Math. Gen

Scientific paper

10.1088/0305-4470/38/17/006

We demonstrate that a Langevin equation that describes the motion of a Brownian particle under non-equilibrium conditions can be exactly transformed to a special equation that explicitly exhibits the response of the velocity to a time dependent perturbation. This transformation is constructed on the basis of an operator formulation originally used in nonlinear perturbation theory for differential equations by extending it to stochastic analysis. We find that the obtained expression is useful for the calculation of fundamental quantities of the system, and that it provides a physical basis for the decomposition of the forces in the Langevin description into effective driving, dissipative, and random forces in a large-scale description.

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