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arXiv 2004.097752020-04-21cond-mat.stat-mechphysics.bio-phq-bio.QM

Lévy walk dynamics in an external harmonic potential

Pengbo Xu, Tian Zhou, Ralf Metzler, Weihua Deng

备注：: 13 pages, 5 figures, RevTeX
发表信息：: Phys. Rev. E 101, 062127 (2020)
DOI：: 10.1103/PhysRevE.101.062127

英文摘要：

Lévy walks (LWs) are spatiotemporally coupled random-walk processes describing superdiffusive heat conduction in solids, propagation of light in disordered optical materials, motion of molecular motors in living cells, or motion of animals, humans, robots, and viruses. We here investigate a key feature of LWs, their response to an external harmonic potential. In this generic setting for confined motion we demonstrate that LWs equilibrate exponentially and may assume a bimodal stationary distribution. We also show that the stationary distribution has a horizontal slope next to a reflecting boundary placed at the origin, in contrast to correlated superdiffusive processes. Our results generalize LWs to confining forces and settle some long-standing puzzles around LWs.

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