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Condensed Matter > Statistical Mechanics
Title: Asymptotic densities of planar Lévy walks: a non-isotropic case
(Submitted on 5 Jul 2021 (v1), last revised 11 Jul 2021 (this version, v3))
Abstract: L\'{e}vy walks are a particular type of continuous-time random walks which results in a super-diffusive spreading of an initially localized packet. The original one-dimensional model has a simple schematization that is based on starting a new unidirectional motion event either in the positive or in the negative direction. We consider two-dimensional generalization of L\'{e}vy walks in the form of the so-called XY-model. It describes a particle moving with a constant velocity along one of the four basic directions and randomly switching between them when starting a new motion event. We address the ballistic regime and derive solutions for the asymptotic density profiles. The solutions have a form of first-order integrals which can be evaluated numerically. For specific values of parameters we derive an exact expression. The analytic results are in perfect agreement with the results of finite-time numerical samplings.
Submission history
From: Sergey Denisov [view email][v1] Mon, 5 Jul 2021 11:40:37 GMT (2950kb,D)
[v2] Tue, 6 Jul 2021 07:58:20 GMT (2950kb,D)
[v3] Sun, 11 Jul 2021 11:48:18 GMT (2040kb,D)
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