Classical and quantum diffusion in the presence of velocity-dependent coupling

Abstract

A generalized system-plus-reservoir model is introduced, which includes four kinds of couplings between the coordinates and velocities of a system and its environment. It is found that the velocity-dependent coupling is not equivalent to a coordinate coupling due to the different power spectra of thermal noise. Harmonic velocity and acceleration noises are proposed which correspond to the coordinate-velocities and velocity-velocities couplings, respectively, if the environmental oscillators are assumed to have a harmonic spectral distribution. Indeed, the velocity-dependent coupling can induce ballistic diffusion of a force-free particle and the mean square velocity depends on the initial preparation. Quantum ballistic diffusion is also presented and its velocity correlation function is found to be unstable at any time. One of real examples of velocity-coordinates coupling is a one-electron atom interacting with the radiation field. A particle moving in a periodic potential shows a nonergodic behavior.