First passage time distributions of anomalous biased diffusion with double absorbing barriers

Guo, Gang; Qiu, Xiaogang

doi:10.1016/j.physa.2014.06.003

Cited by 1 publication

(2 citation statements)

References 31 publications

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“…For a non-Markovian SE (see Refs. [29,[55][56][57] for examples) which involves memory kernels and thus has higher dimension in time, the FPTD can be applied straightforwardly [27,29,31]. Therefore, and due to the similarity between WTD and FPTD we expect that the identification of the WTD with the probability current remains intact.…”

Section: Discussionmentioning

confidence: 99%

“…Our approach is inspired from the calculation [26] of the first passage time distribution (FPTD) [27][28][29][30][31]; indeed, the two quantities are closely related when we assume the dynamics to be Markovian (i.e., time-homogeneous). For symmetric situations our WTD becomes, in fact, identical to the FPTD; however, it is more general than the FPTD in that it allows for directional resolution in asymmetric, continuous situations.…”

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confidence: 99%

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Waiting time distribution for continuous stochastic systems

2014

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The waiting time distribution (WTD) is a common tool for analyzing discrete stochastic processes in classical and quantum systems. However, there are many physical examples where the dynamics is continuous and only approximately discrete, or where it is favourable to discuss the dynamics on a discretized and a continuous level in parallel. An example is the hindered motion of particles through potential landscapes with barriers. In the present paper we propose a consistent generalization of the WTD from the discrete case to situations where the particles perform continuous barrier crossing characterized by a finite duration. To this end, we introduce a recipe to calculate the WTD from the Fokker-Planck (Smoluchowski) equation. In contrast to the closely related first passage time distribution (FPTD), which is frequently used to describe continuous processes, the WTD contains information about the direction of motion. As an application, we consider the paradigmatic example of an overdamped particle diffusing through a washboard potential. To verify the approach and to elucidate its numerical implications, we compare the WTD defined via the Smoluchowski equation with data from direct simulation of the underlying Langevin equation and find full consistency provided that the jumps in the Langevin approach are defined properly. Moreover, for sufficiently large energy barriers, the WTD defined via the Smoluchowski equation becomes consistent with that resulting from the analytical solution of a (two-state) master equation model for the short-time dynamics developed previously by us [Phys. Rev. E 86, 061135 (2012)]. Thus, our approach "interpolates" between these two types of stochastic motion. We illustrate our approach for both symmetric systems and systems under constant force.

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