Absence of stationary states and non-Boltzmann distributions of fractional Brownian motion in shallow external potentials

Abstract

We study the diffusive motion of a particle in a subharmonic potential of the form U ( x ) = | x | ^c (0 2(1 − 1/ α ) holds. We analyse the motion in terms of the mean squared displacement and (when it exists) the stationary probability density function. Moreover we discuss analogies of non-stationarity of Lévy flights in shallow external potentials.

Keywords

• diffusion
• Boltzmann distribution
• fractional Brownian motion