TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.3.3.018
TI  - Unifying description of the damping regimes of a stochastic particle in a periodic potential
PY  - 2017/09/04
UR  - https://scipost.org/SciPostPhys.3.3.018
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 3
IS  - 3
SP  - 018
A1  - Piscitelli, Antonio
AU  - Pica Ciamarra, Massimo
AB  - We analyze the classical problem of the stochastic dynamics of a particle confined in a periodic potential, through the so called Il'in and Khasminskii model, with a novel semi-analytical approach. Our approach gives access to the transient and the asymptotic dynamics in all damping regimes, which are difficult to investigate in the usual Brownian model. We show that the crossover from the overdamped to the underdamped regime is associated with the loss of a typical time scale and of a typical length scale, as signaled by the divergence of the probability distribution of a certain dynamical event. In the underdamped regime, normal diffusion coexists with a non Gaussian displacement probability distribution for a long transient, as recently observed in a variety of different systems. We rationalize the microscopic physical processes leading to the non-Gaussian behavior, as well as the timescale to recover the Gaussian statistics. The theoretical results are supported by numerical calculations and are compared to those obtained for the Brownian model.
ER  -

@Article{10.21468/SciPostPhys.3.3.018,
	title={{Unifying description of the damping regimes of a stochastic particle in a periodic potential}},
	author={Antonio Piscitelli and Massimo Pica Ciamarra},
	journal={SciPost Phys.},
	volume={3},
	pages={018},
	year={2017},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.3.3.018},
	url={https://scipost.org/10.21468/SciPostPhys.3.3.018},
}