Influence of external potentials on heterogeneous diffusion processes

Abstract

In this paper we consider heterogeneous diffusion processes with the power-law dependence of the diffusion coefficient on the position and investigate the influence of external forces on the resulting anomalous diffusion. The heterogeneous diffusion processes can yield subdiffusion as well as superdiffusion, depending on the behavior of the diffusion coefficient. We assume that not only the diffusion coefficient but also the external force has a power-law dependence on the position. We obtain analytic expressions for the transition probability in two cases: when the power-law exponent in the external force is equal to 2eta-1, where 2eta is the power-law exponent in the dependence of the diffusion coefficient on the position, and when the external force has a linear dependence on the position. We found that the power-law exponent in the dependence of the mean square displacement on time does not depend on the external force, this force changes only the anomalous diffusion coefficient. In addition, the external force having the power-law exponent different from 2eta-1 limits the time interval where the anomalous diffusion occurs. We expect that the results obtained in this paper may be relevant for a more complete understanding of anomalous diffusion processes.

References in corpus (31)

• In vivo anomalous diffusion and weak ergodicity breaking of lipid granules
• State-dependent diffusion: thermodynamic consistency and its path integral formulation
• Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes
• Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins
• Diffusion, subdiffusion, and trapping of active particles in heterogeneous media
• Lévy flights in random environments
• Observation of anomalous diffusion and fractional self-similarity in one dimension
• Fractional Fokker--Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises
• Influence of Noise on Force Measurements
• Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes
• Lévy flights of photons in hot atomic vapours
• Non-ergodicity, fluctuations, and criticality in heterogeneous diffusion processes
• Improved estimation of anomalous diffusion exponents in single particle tracking experiments
• Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity
• Prediction of anomalous diffusion and algebraic relaxations for long-range interacting systems, using classical statistical mechanics
• Random Walks in Logarithmic and Power-Law Potentials, Nonuniversal Persistence, and Vortex Dynamics in the Two-Dimensional XY Model
• 1/f noise from nonlinear stochastic differential equations
• Cages and anomalous diffusion in vibrated dense granular media
• Particle dynamics in two-dimensional random energy landscapes - experiments and simulations
• Nonlinear stochastic models of 1/f noise and power-law distributions
• Excitable human dynamics driven by extrinsic events in massive communities
• First-passage and first-exit times of a Bessel-like stochastic process
• A long-range memory stochastic model of the return in financial markets
• Stochastic nonlinear differential equation generating 1/f noise
• Fokker-Planck equation with variable diffusion coefficient in the Stratonovich approach
• Nonlinear inhomogeneous Fokker-Planck equation within a generalized Stratonovich prescription
• Time evolution towards q-Gaussian stationary states through unified Ito-Stratonovich stochastic equation
• Power-law statistics in the velocity fluctuations of Brownian particle in inhomogeneous media and driven by colored noise
• Anomalous diffusion in nonhomogeneous media: Time-subordinated Langevin equation approach
• Looking into DNA breathing dynamics via quantum physics
• 1/f noise from point process and time-subordinated Langevin equations

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