Viscoelastic subdiffusion in a random Gaussian environment

Abstract

Viscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in a random Gaussian environment modeled by stationary Gaussian potentials with decaying spatial correlations. This anomalous diffusion is archetypal for living cells, where cytoplasm is known to be viscoelastic and a spatial disorder also naturally emerges. We obtain some first important insights into it within a model one-dimensional study. Two basic types of potential correlations are studied: short-range exponentially decaying and algebraically slow decaying with an infinite correlation length, both for a moderate (several $k_{B}T$, in the units of thermal energy), and strong (5-10 $k_{B}T$) disorder. For a moderate disorder, it is shown that on the ensemble level viscoelastic subdiffusion can easily overcome the medium's disorder. Asymptotically, it is not distinguishable from the disorder-free subdiffusion. However, a strong scatter in single-trajectory averages is nevertheless seen even for a moderate disorder. It features a weak ergodicity breaking, which occurs on a very long yet transient time scale. Furthermore, for a strong disorder, a very long transient regime of logarithmic, Sinai-type diffusion emerges. It can last longer and be faster in the absolute terms for weakly decaying correlations as compare with the short-range correlations. Residence time distributions in a finite spatial domain are of a generalized log-normal type and are reminiscent also of a stretched exponential distribution. They can be easily confused for power-law distributions in view of the observed weak ergodicity breaking. This suggests a revision of some experimental data and their interpretation.

References in corpus (17)

• Anomalous transport in the crowded world of biological cells
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Fractional Langevin Equation: Over-Damped, Under-Damped and Critical Behaviors
• Fractional diffusion modeling of ion channel gating
• The long reach of DNA sequence heterogeneity in diffusive processes
• Fractional Fokker-Planck dynamics: Numerical algorithm and simulations
• Power spectral density of a single Brownian trajectory: What one can and cannot learn from it
• Use and Abuse of a Fractional Fokker-Planck Dynamics for Time-Dependent Driving
• Anomalous features of diffusion in corrugated potentials with spatial correlations: faster than normal, and other surprises
• Universal fluctuations in subdiffusive transport
• Markovian embedding of fractional superdiffusion
• Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder
• Experimental creation and characterization of random potential energy landscapes exploiting speckle patterns
• Anomalous transport of subdiffusing cargos by single kinesin motors: the role of mechanochemical coupling and anharmonicity of tether
• Fractional Fokker-Planck subdiffusion in alternating fields
• Persistent Sinai type diffusion in Gaussian random potentials with decaying spatial correlations
• Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model

Cited by in corpus (4)

• Long-time persistence of hydrodynamic memory boosts microparticle transport
• Finite-range viscoelastic subdiffusion in disordered systems with inclusion of inertial effects
• A mini-review of the diffusion dynamics of DNA-binding proteins: Experiments and models
• Fractional electron transfer kinetics and a quantum breaking of ergodicity