The linear response approach to the Fokker-Planck equation; 2: A nonlinear stochastic booster

Journal Article · Wed Apr 20 04:00:00 EDT 1994 · International Journal of Modern Physics B; (United States)

DOI:https://doi.org/10.1142/S0217979294000579· OSTI ID:6974278

Bianucci, M ^[1]; Mannella, R; Grigolini, P ^[2]; West, B J ^[3]

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1. GNSM del CNR, Pisa (Italy). Dipt. di Fisica Univ. di Pavia (Italy). Dipt. di Fisica
2. GNSM del CNR, Pisa (Italy). Dipt. di Fisica
3. Univ. of North Texas, Denton, TX (United States). Dept. of Physics

It has been pointed out in part 1 that the friction resulting from the interaction between a Brownian particle and a nonlinear bath cannot in general be evaluated by a second-order perturbation treatment with the conventional Liouville or Liouville-like approach. It has also been shown that a convenient way of proceeding is to express the dynamics of the bath within a master equation approach, which makes it possible to apply a linear response treatment (LRT) also in the case of a nonlinear bath. They check the internal consistency of this theory using as a bath for the velocity w of the Brownian particle a doorway variable [xi], which executes random jumps among some discrete values. In this specific condition the explicit expression for the master equation driving the motion of the bath is easily derived. It is also relatively easy to check the predictions of the theory with computer calculations. The internal consistency of the theory is proved and the agreement with the numerical calculation is shown to be remarkably good in the parameter region where the LRT approach is expected to hold.

• OSTI ID: 6974278
• Journal Information: International Journal of Modern Physics B; (United States), Journal Name: International Journal of Modern Physics B; (United States) Vol. 8:9; ISSN IJPBEV; ISSN 0217-9792
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BROWNIAN MOVEMENT
DIFFERENTIAL EQUATIONS
EQUATIONS
FOKKER-PLANCK EQUATION
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
STOCHASTIC PROCESSES