THE LINEAR-RESPONSE APPROACH TO THE FOKKER-PLANCK EQUATION .2. A NONLINEAR STOCHASTIC BOOSTER

It has been pointed out in I1 that the friction resulting from the int eraction between a Brownian particle and a nonlinear bath cannot in ge neral be evaluated by a second-order perturbation treatment with the c onventional Liouville or Liouville-like approach. It has also been sho wn that a convenient way of proceeding is to express the dynamics of t he bath within a master equation approach, which makes it possible to apply a linear response treatment (LRT) also in the case of a nonlinea r bath. We check the internal consistency of this theory using as a ba th for the velocity w of the Brownian particle a doorway variable xi, which executes random jumps among some discrete values. In this specif ic condition the explicit expression for the master equation driving t he motion of the bath is easily derived. It is also relatively easy to check the predictions of the theory with computer calculations. The i nternal 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.