Sub-diffusion in External Potential: Anomalous hiding behind Normal

Abstract

We propose a model of sub-diffusion in which an external force is acting on a particle at all times not only at the moment of jump. The implication of this assumption is the dependence of the random trapping time on the force with the dramatic change of particles behavior compared to the standard continuous time random walk model. Constant force leads to the transition from non-ergodic sub-diffusion to seemingly ergodic diffusive behavior. However, we show it remains anomalous in a sense that the diffusion coefficient depends on the force and the anomalous exponent. For the quadratic potential we find that the anomalous exponent defines not only the speed of convergence but also the stationary distribution which is different from standard Boltzmann equilibrium.

6 pages, 3 figures

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• Feynman-Kac equation for anomalous processes with space- and time-dependent forces
• Non-Markovian intracellular transport with sub-diffusion and run-length dependent detachment rate
• Langevin formulation of a subdiffusive continuous time random walk in physical time
• Langevin picture of Lévy walk in a constant force field
• Langevin picture of anomalous diffusion processes in expanding medium
• Random diffusivity processes in an external force field
• A non-linear subdiffusion model for a cell-cell adhesion in chemotaxis
• Density-Dependence Subdiffusion in Chemotaxis