Giant diffusion and coherent transport in tilted periodic inhomogeneous systems

TL;DR

This paper studies how a Brownian particle's diffusion and transport are affected by a space-dependent friction in a tilted periodic potential, revealing regimes of enhanced or suppressed diffusion and conditions for coherent transport.

Contribution

It provides analytical expressions for current and diffusion in inhomogeneous systems and uncovers counter-intuitive effects of noise on diffusion and transport coherence.

Findings

Diffusion coefficient can be maximized near critical threshold $F_c$

Increasing temperature can decrease diffusion in certain regimes

Large mean velocity with small diffusion indicates coherent transport

Abstract

We investigate the dynamics of an overdamped Brownian particle moving in a washboard potential with space dependent friction coefficient. Analytical expressions have been obtained for current and diffusion coefficient. We show that the effective diffusion coefficient can be enhanced or suppressed compared to that of the uniform friction case. The diffusion coefficient is maximum near the critical threshold ($F_{c}$), which is sensitive to temperature and the frictional profile. In some parameter regime we observe that increase in noise (temperature) decreases the diffusion, which is counter-intuitive. This leads to coherent transport with large mean velocity accompanied by small diffusion. This is shown explicitly by analysis of P\'{e}clet number, which has been introduced to study coherent or optimal transport. This phenomena is complementary to giant diffusion.