Drift-Controlled Anomalous Diffusion: A Solvable Gaussian Model

Details Drift-Controlled Anomalous Diffusion: A Solvable Gaussian Model Drift-Controlled Anomalous Diffusion: A Solvable Gaussian Model

2000-01-14

arxiv.org/abs/cond-mat/0001211v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 1 figure

Scientific paper

10.1103/PhysRevE.61.R4675

We introduce a Langevin equation characterized by a time dependent drift. By assuming a temporal power-law dependence of the drift we show that a great variety of behavior is observed in the dynamics of the variance of the process. In particular diffusive, subdiffusive, superdiffusive and stretched exponentially diffusive processes are described by this model for specific values of the two control parameters. The model is also investigated in the presence of an external harmonic potential. We prove that the relaxation to the stationary solution is power-law in time with an exponent controlled by one of model parameters.

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