The Mathematical Institute, University of Oxford, Eprints Archive

Transient aging in fractional Brownian and Langevin-equation motion

Kursawe, J and Schulz, J and Metzler, R (2013) Transient aging in fractional Brownian and Langevin-equation motion. Physical Review E, 88 . 062124.

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Abstract

Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin-equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion and fractional Langevin-equation motion under external confinement are transiently nonergodic—time and ensemble averages behave differently—from the moment when the particle starts to sense the confinement. Here we show that these processes also exhibit transient aging, that is, physical observables such as the time-averaged mean-squared displacement depend on the time lag between the initiation of the system at time t=0 and the start of the measurement at the aging time ta. In particular, it turns out that for fractional Langevin-equation motion the aging dependence on ta is different between the cases of free and confined motion. We obtain explicit analytical expressions for the aged moments of the particle position as well as the time-averaged mean-squared displacement and present a numerical analysis of this transient aging phenomenon.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1774
Deposited By: Sara Jolliffe
Deposited On:12 Feb 2014 08:50
Last Modified:29 May 2015 19:28

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