We study the stability of the Maxwell–Boltzmann (i.e., Gaussian) distribution for the density of states at equilibrium, against an arbitrary choice of the friction in the Langevin equation. We find that this distribution is Gaussian, if and only if the friction is Lipschitz continuous. In...

We report the study of the one-time and two-time quantum dynamics of the Brownian particle coupled to a thermal bath of fractal dimension 0δ2. The autocorrelation of the position can be defined only if the particle is localized (T=0,0δ1), in which case the position thermalizes. On another...