Theory of relaxation dynamics for anomalous diffusion processes in harmonic potential

Abstract

Optical tweezers setup is often used to probe the motion of individual tracer particle, which promotes the study of relaxation dynamics of a generic process confined in a harmonic potential. We uncover the dependence of ensemble- and time-averaged mean square displacements of confined processes on the velocity correlation function $C(t,t+\tau )$ of the original process. With two different scaling forms of $C(t,t+\tau )$ for small $\tau$ and large $\tau$, the stationary value and the relaxation behaviors can be obtained immediately. The gotten results are valid for a large amount of anomalous diffusion processes, including fractional Brownian motion, scaled Brownian motion, and the multi-scale Lévy walk with different exponents of running time distribution.

arXiv comment5 pages, 3 figures

References in corpus (29)

• Active Particles in Complex and Crowded Environments
• Lévy walks
• In vivo anomalous diffusion and weak ergodicity breaking of lipid granules
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Ergodic Properties of Fractional Brownian-Langevin Motion
• Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• Foundation of Fractional Langevin Equation: Harmonization of a Many Body Problem
• Aging Continuous Time Random Walks
• Inequivalence of time and ensemble averages in ergodic systems: exponential versus power-law relaxation in confinement
• Scaled Brownian motion as a mean field model for continuous time random walks
• From the area under the Bessel excursion to anomalous diffusion of cold atoms
• Non-normalizable densities in strong anomalous diffusion: beyond the central limit theorem
• Finite-time effects and ultraweak ergodicity breaking in superdiffusive dynamics
• Time averaged Einstein relation and fluctuating diffusivities for the Lévy walk
• Aging Wiener-Khinchin Theorem
• Infinite densities for Lévy walks
• Random time averaged diffusivities for Lévy walks
• Wiener-Khinchin theorem for nonstationary scale-invariant processes
• Localization and ballistic diffusion for the tempered fractional Brownian-Langevin motion
• Langevin dynamics with dichotomous noise; direct simulation and applications
• Scaling Green-Kubo relation and application to three aging systems
• Lévy-walk-like Langevin dynamics
• Subdiffusion in an external force field
• Scale invariant Green-Kubo relation for time averaged diffusivity
• Aging two-state process with Lévy walk and Brownian motion
• Langevin dynamics for Lévy walk with memory
• Langevin picture of Lévy walk in a constant force field
• Strong anomalous diffusion in two-state process with Lévy walk and Brownian motion

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