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Unifying description of the damping regimes of a stochastic particle in a periodic potential
by Antonio Piscitelli, Massimo Pica Ciamarra
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Submission summary
| Authors (as registered SciPost users): | Massimo Pica Ciamarra · Antonio Piscitelli |
| Submission information | |
|---|---|
| Preprint Link: | http://arxiv.org/abs/1705.08083v2 (pdf) |
| Date accepted: | 2017-08-26 |
| Date submitted: | 2017-08-18 02:00 |
| Submitted by: | Piscitelli, Antonio |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
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.
List of changes
In the revised version of the manuscript :
-In Sec.2 we introduced the Il'in Kashminskii equation of
motion when reviewing previous results. We specified more
precisely the model
-We eliminated the acronym VhD for Van Hove, substituting
with the explicit expression, and reduced the number of acronyms to
improve clarity
- We eliminated the inset in panel c of Fig 7. We have also modified
panels (d-f) of Fig. 7 to improve their readability
-We modified the first sentence in the abstract and the first sentence of Sec. IIIb
-We corrected the label in Fig. 2a
-We corrected a sentence in Sec. 5a and introduced a comment at the end of Sec. 4
-We corrected Eq.20 and introduced Eq.19
-We corrected few typos
Published as SciPost Phys. 3, 018 (2017)