Title: Transition of multi-diffusive states in a biased periodic potential,
Abstract: We study a frequency-dependent damping model of hyper-diffusion within the
generalized Langevin equation. The model allows for the colored noise defined
by its spectral density, assumed to be proportional to $\omega^{\delta-1}$ at
low frequencies with $0<\delta<1$ (sub-Ohmic damping) or $1<\delta<2$
(super-Ohmic damping), where the frequency-dependent damping is deduced from
the noise by means of the fluctuation-dissipation theorem. It is shown that for
super-Ohmic damping and certain parameters, the diffusive process of the
particle in a titled periodic potential undergos sequentially four
time-regimes: thermalization, hyper-diffusion, collapse and asymptotical
restoration. For analysing transition phenomenon of multi-diffusive states, we
demonstrate that the first exist time of the particle escaping from the locked
state into the running state abides by an exponential distribution. The concept
of equivalent velocity trap is introduced in the present model, moreover,
reformation of ballistic diffusive system is also considered as a marginal
situation, however there does not exhibit the collapsed state of diffusion.