Scaled Brownian motion as a mean field model for continuous time random walks

Abstract

We consider scaled Brownian motion (sBm), a random process described by a diffusion equation with explicitly time-dependent diffusion coefficient $D(t)=D_0{t}^{\alpha -1}$ (Batchelor's equation) which, for $\alpha <1$, is often used for fitting experimental data for subdiffusion of unclear genesis. We show that this process is a close relative of subdiffusive continuous-time random walks and describes the motion of the center of mass of a cloud of independent walkers. It shares with subdiffusive CTRW its non-stationary and non-ergodic properties. The non-ergodicity of sBm does not however go hand in hand with strong difference between its different realizations: its heterogeneity ("ergodicity breaking") parameter tends to zero for long trajectories.

4 pages, 1 figure, submitted to Phys. Rev. E (Brief Report)

References in corpus (2)

• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Model of lateral diffusion in ultrathin layered films

Cited by in corpus (40)

• Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities
• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• Non-universal tracer diffusion in crowded media of non-inert obstacles
• Non-ergodicity, fluctuations, and criticality in heterogeneous diffusion processes
• Scaled Brownian motion with renewal resetting
• Non-renewal resetting of scaled Brownian motion
• Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes
• Quantifying the non-ergodicity of scaled Brownian motion
• Nonergodic dynamics of force-free granular gases
• Aging Scaled Brownian Motion
• Ageing underdamped scaled Brownian motion: ensemble and time averaged particle displacements, non-ergodicity, and the failure of the overdamping approximation
• Weak ergodicity breaking in an anomalous diffusion process of mixed origins
• Localization and universal fluctuations in ultraslow diffusion processes
• Solvable random walk model with memory and its relations with Markovian models of anomalous diffusion
• First passage statistics for aging diffusion in annealed and quenched disorder
• Wiener-Khinchin theorem for nonstationary scale-invariant processes
• Single-trajectory spectral analysis of scaled Brownian motion
• Continuous time random walks under power-law resetting
• Ergodicity breaking and particle spreading in noisy heterogeneous diffusion processes
• Anomalous diffusion in a quenched-trap model on fractal lattices
• Moses, Noah and Joseph Effects in Coupled Lévy Processes
• Diffusion in an expanding medium: Fokker-Planck equation, Green's function and first-passage properties
• Bayesian inference of scaled versus fractional Brownian motion
• Optimization of random search processes in the presence of an external bias
• Scale invariant Green-Kubo relation for time averaged diffusivity
• Elucidating fluctuating diffusivity in center-of-mass motion of polymer models with time-averaged mean-square-displacement tensor
• Ergodic property of random diffusivity system with trapping events
• Ergodic property of Langevin systems with superstatistical, uncorrelated or correlated diffusivity
• Langevin formulation of a subdiffusive continuous time random walk in physical time
• Time-fractional Caputo derivative versus other integro-differential operators in generalized Fokker-Planck and generalized Langevin equations
• Anomalous diffusion and FRAP dynamics in the random comb model
• Langevin picture of anomalous diffusion processes in expanding medium
• Nonergodicity of $d$-dimensional generalized Lévy walks and their relation to other space-time coupled models
• Theory of relaxation dynamics for anomalous diffusion processes in harmonic potential
• Non-stationary Markovian Replication Process causing Diverse Diffusions
• First-passage dynamics of obstructed tracer particle diffusion in one-dimensional systems
• Anomalous diffusion of scaled Brownian tracers
• Time-Average Based on Scaling Law in Anomalous Diffusions
• Complete Decomposition of Anomalous Diffusion in Variable Speed Generalized Lévy Walks
• Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion