Random walks on intersecting geometries - Kölner UniversitätsPublikationsServer

Sepehrinia, Reza, Saberi, Abbas Ali ORCID: 0000-0001-8864-4748 and Dashti-Naserabadi, Hor (2019). Random walks on intersecting geometries. Phys. Rev. E, 100 (2). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2470-0053

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DOI:10.1103/PhysRevE.100.022144

Abstract

We present an analytical approach to study simple symmetric random walks on a crossing geometry consisting of a plane square lattice crossed by n(1) number of lines that all meet each other at a single point (the origin) on the plane. The probability density to find the walker at a given distance from the origin either in a line or in the plane geometry is exactly calculated as a function of time t. We find that the large-time asymptotic behavior of the walker for any arbitrary number n(l) of lines is eventually governed by the diffusion of the walker on the plane after a crossover time approximately given by t(c) proportional to n(l)(2). We show that this competition can be changed in favor of the line geometry by switching on an arbitrarily small perturbation of a drift term in which even a weak biased walk is able to drain the whole probability density into the line at long-time limit. We also present the results of our extensive simulations of the model which perfectly support our analytical predictions. Our method can, however, be simply extended to other crossing geometries with a single common point.

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Sepehrinia, Reza	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Saberi, Abbas Ali	UNSPECIFIED	orcid.org/0000-0001-8864-4748	UNSPECIFIED
Dashti-Naserabadi, Hor	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED