Memory-induced diffusive-superdiffusive transition: Ensemble and time-averaged observables

Adrián A. Budini
Phys. Rev. E 95, 052110 – Published 8 May 2017

Abstract

The ensemble properties and time-averaged observables of a memory-induced diffusive-superdiffusive transition are studied. The model consists in a random walker whose transitions in a given direction depend on a weighted linear combination of the number of both right and left previous transitions. The diffusion process is nonstationary, and its probability develops the phenomenon of aging. Depending on the characteristic memory parameters, the ensemble behavior may be normal, superdiffusive, or ballistic. In contrast, the time-averaged mean squared displacement is equal to that of a normal undriven random walk, which renders the process nonergodic. In addition, and similarly to Lévy walks [Godec and Metzler, Phys. Rev. Lett. 110, 020603 (2013)], for trajectories of finite duration the time-averaged displacement apparently become random with properties that depend on the measurement time and also on the memory properties. These features are related to the nonstationary power-law decay of the transition probabilities to their stationary values. Time-averaged response to a bias is also calculated. In contrast with Lévy walks [Froemberg and Barkai, Phys. Rev. E 87, 030104(R) (2013)], the response always vanishes asymptotically.

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  • Received 23 February 2017
  • Revised 5 April 2017

DOI:https://doi.org/10.1103/PhysRevE.95.052110

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Statistical Physics & Thermodynamics

Authors & Affiliations

Adrián A. Budini

  • Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Centro Atómico Bariloche, Avenida E. Bustillo Km 9.5, (8400) Bariloche, Argentina and Universidad Tecnológica Nacional (UTN-FRBA), Fanny Newbery 111, (8400) Bariloche, Argentina

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Issue

Vol. 95, Iss. 5 — May 2017

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