Generalized Langevin equations: Anomalous diffusion and probability distributions
Open Access
- 1 June 1996
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 53 (6) , 5872-5881
- https://doi.org/10.1103/physreve.53.5872
Abstract
We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions. © 1996 The American Physical Society.Keywords
This publication has 12 references indexed in Scilit:
- Free inertial processes driven by Gaussian noise: Probability distributions, anomalous diffusion, and fractal behaviorPhysical Review E, 1995
- Second-order dichotomous processes: Damped free motion, critical behavior, and anomalous superdiffusionPhysical Review E, 1993
- Anomalous diffusion in the Kuramoto-Sivashinsky equationPhysical Review Letters, 1993
- Long-time-correlation effects and biased anomalous diffusionPhysical Review A, 1992
- Second-order processes driven by dichotomous noisePhysical Review A, 1992
- Long-time correlation effects and fractal Brownian motionPhysics Letters A, 1990
- Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applicationsPhysics Reports, 1990
- Anomalous diffusion: A dynamic perspectivePhysica A: Statistical Mechanics and its Applications, 1990
- Diffusion in disordered mediaAdvances in Physics, 1987
- Asymptotic Expansion of Laplace Convolutions for Large Argument and Tail Densities for Certain Sums of Random VariablesSIAM Journal on Mathematical Analysis, 1974