Title:	First-passage time: Lattice versus continuum
Authors:	Sharma, Kamal Kumar, N.
Issue Date:	11-Sep-2012
Publisher:	American Physical Society
Citation:	Physical Review E, 2012, Vol.86, p032104
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.
Description:	Restricted Access.
URI:	http://hdl.handle.net/2289/5695
ISSN:	1539-3755 1550-2376 (Online)
Alternative Location:	http://dx.doi.org/10.1103/PhysRevE.86.032104 http://adsabs.harvard.edu/abs/2012PhRvE..86c2104S
Copyright:	2013 American Physical Society
Appears in Collections:	Research Papers (TP)

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