  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.
