It has been pointed out in I1 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. We 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.
THE LINEAR-RESPONSE APPROACH TO THE FOKKER-PLANCK EQUATION .2. A NONLINEAR STOCHASTIC BOOSTER
MANNELLA, RICCARDO;
1994-01-01
Abstract
It has been pointed out in I1 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. We 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
