Giant increase of diffusion by small rise of friction

TL;DR

This paper investigates an unusual phenomenon where increasing friction in a driven inertial Brownian particle system can dramatically amplify diffusion, contrary to typical expectations, due to bifurcation mechanisms and orbit population changes.

Contribution

It reveals the counterintuitive giant increase in diffusion with friction in a specific driven system and explains the underlying bifurcation and orbit population dynamics.

Findings

Diffusion can increase up to five orders of magnitude with doubled friction.

Bifurcation of periodic orbits causes the giant diffusion enhancement.

In weak dissipation, non-monotonic orbit population changes also enhance diffusion.

Abstract

Diffusion coefficient usually decreases when friction increases. We analyze the opposite behavior in the paradigmatic system consisting of an inertial Brownian particle moving in a symmetric spatially periodic potential and driven by an unbiased time periodic force. For tailored parameter set in strong dissipation regime the particle spreading can be giantly amplified: if the friction is twice as large then the diffusion grows up to five orders of magnitude. The mechanism lying behind this effect is related to bifurcation of periodic orbits oscillating around the potential maximum and their symmetric displacement towards the adjacent potential minima when the friction coefficient increases. On the other hand, in the weak dissipation regime, where the increase of diffusion vs friction is also observed, the effect is induced by a non-monotonic change of population of the running orbits. However, in this regime the enhancement of diffusion is much smaller.