First-passage time: lattice versus continuum

Sharma, Kamal ; Kumar, N. (2012) First-passage time: lattice versus continuum Physical Review E, 86 (3). 032104_1-032104_4. ISSN 1539-3755

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Official URL: http://dx.doi.org/10.1103/PhysRevE.86.032104

Related URL: http://dx.doi.org/10.1103/PhysRevE.86.032104

Abstract

The well known approach, based on Schrödinger's integral equation, to the problem of calculating the first-passage probability density in time for classical diffusion on a continuum is revisited for the case of diffusion by hopping on a discrete lattice. It turns out that a certain boundary condition central to solving the integral equation, invoked first by Schrödinger and then by others on the basis of a physical argument, needs to be modified for the discrete case. In fact, the required boundary condition turns out to be determined entirely by the normalization condition for the first-passage probability density. An explicit analytical expression is derived for the first-passage density for a three-site problem modeling escape over a barrier. The related quantum first-passage problem is also commented upon briefly.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:96402
Deposited On:18 Dec 2012 07:04
Last Modified:08 Feb 2013 09:19

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