Brownian motion with linear and quadratic friction

Abstract

We study Brownian motion in a medium in which a frictional force varying quadratically as the velocity acts on the particle. We solve the approximate time-dependent propagator by obtaining the eigenfunctions and eigenvalues of the Fokker-Planck equation using Riccati-Pad Ìe method. High noise limit resulted in dominance of quadratic friction with eigen-states related to a potential studied in supersymmetric quantum mechanics.