Diffusion and Superdiffusion in Lattice Models for Colliding Particles with Stored Momentum

Edward Crane; Sean Ledger; Bálint Tóth

doi:10.1007/s10955-019-02419-9

Diffusion and Superdiffusion in Lattice Models for Colliding Particles with Stored Momentum

Edward Crane, Sean Ledger, Bálint Tóth

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Abstract

We introduce two discrete models of a collection of colliding particles with stored momentum and study the asymptotic growth of the mean-square displacement of an active particle. We prove that the models are superdiffusive in one dimension (with power law correction) and diffusive in three and higher dimensions. In two dimensions we demonstrate superdiffusivity (with logarithmic correction) for certain anisotropic initial conditions.

Original language	English
Pages (from-to)	1240-1262
Number of pages	23
Journal	Journal of Statistical Physics
Volume	177
Issue number	6
Early online date	7 Nov 2019
DOIs	https://doi.org/10.1007/s10955-019-02419-9
Publication status	Published - Dec 2019

Keywords

superdiffusion
momentum transport
random walk with memory

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10.1007/s10955-019-02419-9

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title = "Diffusion and Superdiffusion in Lattice Models for Colliding Particles with Stored Momentum",

abstract = "We introduce two discrete models of a collection of colliding particles with stored momentum and study the asymptotic growth of the mean-square displacement of an active particle. We prove that the models are superdiffusive in one dimension (with power law correction) and diffusive in three and higher dimensions. In two dimensions we demonstrate superdiffusivity (with logarithmic correction) for certain anisotropic initial conditions.",

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AU - Ledger, Sean

AU - Tóth, Bálint

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N2 - We introduce two discrete models of a collection of colliding particles with stored momentum and study the asymptotic growth of the mean-square displacement of an active particle. We prove that the models are superdiffusive in one dimension (with power law correction) and diffusive in three and higher dimensions. In two dimensions we demonstrate superdiffusivity (with logarithmic correction) for certain anisotropic initial conditions.

AB - We introduce two discrete models of a collection of colliding particles with stored momentum and study the asymptotic growth of the mean-square displacement of an active particle. We prove that the models are superdiffusive in one dimension (with power law correction) and diffusive in three and higher dimensions. In two dimensions we demonstrate superdiffusivity (with logarithmic correction) for certain anisotropic initial conditions.

KW - superdiffusion

KW - momentum transport

KW - random walk with memory

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DO - 10.1007/s10955-019-02419-9

M3 - Article (Academic Journal)

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JF - Journal of Statistical Physics

SN - 0022-4715

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ER -

Diffusion and Superdiffusion in Lattice Models for Colliding Particles with Stored Momentum

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Dr Edward T Crane

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Diffusion and Superdiffusion in Lattice Models for Colliding Particles with Stored Momentum

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Dr Edward T Crane

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