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

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.

25 pages, 4 figures

References in corpus (5)

• Artificial Brownian motors: Controlling transport on the nanoscale
• Tuned, driven, and active soft matter
• Velocity and diffusion constant of an active particle in a one dimensional force field
• Active Matter Commensuration and Frustration Effects on Periodic Substrates
• Clogging, Dynamics and Reentrant Fluid for Active Matter on Periodic Substrates

Cited by in corpus (1)

• Quantum walk in stochastic environment