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

Dekel Shapira, Doron Cohen

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number063026
JournalNew Journal of Physics
Issue number6
StatePublished - 1 Jun 2022


  • active particles
  • localization
  • non-Hermitian
  • rate equations
  • Sinai model
  • sliding transition

ASJC Scopus subject areas

  • Physics and Astronomy (all)


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