Subdiffusion in an external force field

Abstract

The phenomena of subdiffusion are widely observed in physical and biological systems. To investigate the effects of external potentials, say, harmonic potential, linear potential, and time dependent force, we study the subdiffusion described by subordinated Langevin equation with white Gaussian noise, or equivalently, by the single Langevin equation with compound noise. If the force acts on the subordinated process, it keeps working all the time; otherwise, the force just exerts an influence on the system at the moments of jump. Some common statistical quantities, such as, the ensemble and time averaged mean squared displacement, position autocorrelation function, correlation coefficient, generalized Einstein relation, are discussed to distinguish the effects of various forces and different patterns of acting. The corresponding Fokker-Planck equations are also presented. All the stochastic processes discussed here are non-stationary, non-ergodicity, and aging.

15 pages, 10 figures

References in corpus (26)

• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking
• Langevin equations for continuous time Lévy flights
• The dynamical foundation of fractal stream chemistry: The origin of extremely long retention times
• Fractional Fokker--Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises
• The Einstein relation generalized to non-equilibrium
• Inequivalence of time and ensemble averages in ergodic systems: exponential versus power-law relaxation in confinement
• Joint Probability Distributions for a Class of Non-Markovian Processes
• A fractional Feynman-Kac equation for weak ergodicity breaking
• Linear Response in Complex Systems: CTRW and the Fractional Fokker-Planck Equations
• Continuous-time random-walk model for anomalous diffusion in expanding media
• Localization and ballistic diffusion for the tempered fractional Brownian-Langevin motion
• Subordinated Langevin Equations for Anomalous Diffusion in External Potentials - Biasing and Decoupled Forces
• Anomalous processes with general waiting times: functionals and multi-point structure
• Enhancement, slow relaxation, ergodicity and rejuvenation of diffusion in biased continuous-time random walks
• A fractional diffusion equation for two-point probability distributions of a continuous-time random walk
• Diffusion in an expanding medium: Fokker-Planck equation, Green's function and first-passage properties
• Sub-diffusion in External Potential: Anomalous hiding behind Normal
• Tempered fractional Langevin-Brownian motion with inverse $\beta$-stable subordinator
• First passage time processes and subordinated SLE
• Weak Galilean invariance as a selection principle for coarse-grained diffusive models
• Feynman-Kac equation for anomalous processes with space- and time-dependent forces
• A no-go theorem for ergodicity and an Einstein relation
• Feynman-Kac equation revisited
• Fluctuation relations for anomalous dynamics generated by time-fractional Fokker-Planck equations
• Langevin formulation of a subdiffusive continuous time random walk in physical time

Cited by in corpus (13)

• Nonlocal Diffusion Operators for Normal and Anomalous Dynamics
• Ergodic property of random diffusivity system with trapping events
• Ergodic property of Langevin systems with superstatistical, uncorrelated or correlated diffusivity
• Langevin picture of Lévy walk in a constant force field
• Strong anomalous diffusion in two-state process with Lévy walk and Brownian motion
• Continuous Time Random Walk in a velocity field: Role of domain growth, Galilei-invariant advection-diffusion, and kinetics of particle mixing
• Lévy-walk-like Langevin dynamics affected by a time-dependent force
• Theory of relaxation dynamics for anomalous diffusion processes in harmonic potential
• Langevin picture of anomalous diffusion processes in expanding medium
• The standard and the fractional Ornstein-Uhlenbeck process on a growing domain
• Novel anomalous diffusion phenomena of underdamped Langevin equation with random parameters
• Random diffusivity processes in an external force field
• Numerical algorithm for the model describing anomalous diffusion in expanding media