Persistent correlations in the motion of a Brownian particle interacting with a finite-size random environment

We study the long time evolution of a Brownian particle in a finite-size disordered system. The presence of a random static potential is shown to generate persistent correlations of kinetic energy fluctuations described by fourth-order velocity cumulant functions. We show also that the usual correlations of velocity fluctuations do not vanish at large time, provided that an external bias is applied to the sample. An appearance of persistent correlations is noted to reflect a nonergodic character of the velocity fluctuations.