Emergence of Sinai Physics in the stochastic motion of passive and active particles

TL;DR

This paper explores how Sinai physics, characterized by suppressed diffusion and localization phenomena, emerges in both passive and active particles within disordered environments, highlighting the effects of bias and irradiation.

Contribution

It provides a critical analysis of Sinai physics in active and passive Brownian particles using both tight-binding and Fokker-Planck models, incorporating effects of irradiation-induced bias.

Findings

Diffusion is suppressed in disordered environments with bias.

Dynamics become sub-diffusive and over-damped due to irradiation.

Spontaneous delocalization can occur in finite systems.

Abstract

A particle that is immersed in a uniform temperature bath performs Brownian diffusion, as discussed by Einstein. But Sinai has realized that in a "random environment" the diffusion is suppressed. Follow-up works have pointed out that in the presence of bias $f$ there are delocalization and sliding transitions, with threshold value $f_c$ that depends on the disorder strength. We discuss in a critical way the emergence of Sinai physics for both passive and active Brownian particles. Tight-binding and Fokker-Planck versions of the model are addressed on equal footing. We assume that the transition rates between sites are enhanced either due to a driving mechanism or due to self-propulsion mechanism that are induced by an irradiation source. Consequently, counter intuitively, the dynamics becomes sub-diffusive and the relaxation modes become over-damped. For a finite system, spontaneous delocalization may arise, due to residual bias that is induced by the irradiation.