Persistent Sinai-type diffusion in Gaussian random potentials with decaying spatial correlations

First-passage times in conical varying-width channels biased by a transverse gravitational force: Comparison of analytical and numerical results

We study the crossing time statistic of diffusing point particles between the two ends of expanding and narrowing two-dimensional conical channels under a transverse external gravitational field. The theoretical expression for the mean first-passage time for such a system is derived under the assumption that the axial diffusion in a two-dimensional channel of smoothly varying geometry can be approximately described as a one-dimensional diffusion in an entropic potential with position-dependent effective diffusivity in terms of the modified Fick-Jacobs equation. We analyze the channel crossing dynamics in terms of the mean first-passage time, combining our analytical results with extensive two-dimensional Brownian dynamics simulations, allowing us to find the range of applicability of the one-dimensional approximation. We find that the effective particle diffusivity decreases with increasing amplitude of the external potential. Remarkably, the mean first-passage time for crossing the channel is shown to assume a minimum at finite values of the potential amplitude.

Anomalous transport tuned through stochastic resetting in the rugged energy landscape of a chaotic system with roughness

Stochastic resetting causes kinetic phase transitions, whereas its underlying physical mechanism remains to be elucidated. We here investigate the anomalous transport of a particle moving in a chaotic system with a stochastic resetting and a rough potential and focus on how the stochastic resetting, roughness, and nonequilibrium noise affect the transports of the particle. We uncover the physical mechanism for stochastic resetting resulting in the anomalous transport in a nonlinear chaotic system: The particle is reset to a new basin of attraction which may be different from the initial basin of attraction from the view of dynamics. From the view of the energy landscape, the particle is reset to a new energy state of the energy landscape which may be different from the initial energy state. This resetting can lead to a kinetic phase transition between no transport and a finite net transport or between negative mobility and positive mobility. The roughness and noise also lead to the transition. Based on the mechanism, the transport of the particle can be tuned by these parameters. For example, the combination of the stochastic resetting, roughness, and noise can enhance the transport and tune negative mobility, the enhanced stability of the system, and the resonant-like activity. We analyze these results through variances (e.g., mean-squared velocity, etc.) and correlation functions (i.e., velocity autocorrelation function, position-velocity correlation function, etc.). Our results can be extensively applied in the biology, physics, and chemistry, even social system.

Negative autocorrelations of disorder strongly suppress thermally activated particle motion in short-correlated quenched Gaussian disorder potentials

We evaluate the mean escape time of overdamped particles over potential barriers in short-correlated quenched Gaussian disorder potentials in one dimension at low temperature. The thermally activated escape is very sensitive to the form of the tail of the potential barrier probability distribution. We evaluate this tail by using the optimal fluctuation method. For monotone decreasing autocovariances, we reproduce the tail obtained by Lopatin and Vinokur (2001). However, for nonmonotonic autocovariances of the disorder potential which exhibit negative autocorrelations, we show that the tail is higher. This leads to an exponential increase of the mean escape time. The transition between the two regimes has the character of a first-order transition.

Fingerprints of viscoelastic subdiffusion in random environments: Revisiting some experimental data and their interpretations

Many experimental studies revealed subdiffusion of various nanoparticles in diverse polymer and colloidal solutions, cytosol and plasma membrane of biological cells, which are viscoelastic and, at the same time, highly inhomogeneous randomly fluctuating environments. The observed subdiffusion often combines features of ergodic fractional Brownian motion (reflecting viscoelasticity) and nonergodic jumplike non-Markovian diffusional processes (reflecting disorder). Accordingly, several theories were proposed to explain puzzling experimental findings. Below we show that some of the significant and profound published experimental results are better rationalized within the viscoelastic subdiffusion approach in random environments, which is based on generalized Langevin dynamics in random potentials, than some earlier proposed theories.

The influences of correlated spatially random perturbations on first passage time in a linear-cubic potential

The influences of correlated spatially random perturbations (SRPs) on the first passage problem are studied in a linear-cubic potential with a time-changing external force driven by a Gaussian white noise. First, the escape rate in the absence of SRPs is obtained by Kramers' theory. For the random potential case, we simplify the escape rate by multiplying the escape rate of smooth potentials with a specific coefficient, which is to evaluate the influences of randomness. Based on this assumption, the escape rates are derived in two scenarios, i.e., small/large correlation lengths. Consequently, the first passage time distributions (FPTDs) are generated for both smooth and random potential cases. We find that the position of the maximal FPTD has a very good agreement with that of numerical results, which verifies the validity of the proposed approximations. Besides, with increasing the correlation length, the FPTD shifts to the left gradually and tends to the smooth potential case. Second, we investigate the most probable passage time (MPPT) and mean first passage time (MFPT), which decrease with increasing the correlation length. We also find that the variation ranges of both MPPT and MFPT increase nonlinearly with increasing the intensity. Besides, we briefly give constraint conditions to guarantee the validity of our approximations. This work enables us to approximately evaluate the influences of the correlation length of SRPs in detail, which was always ignored previously.

Anomalously Slow Dewetting of Colloidal Particles at a Liquid/Gas Interface

We consider the anomalously slow dewetting of colloidal particles adsorbed at a liquid/gas interface. The particles move in the vertical direction under the action of a regular capillary force and an irregular force caused by defects (roughness and chemical heterogeneity). The particle diffusion is modeled by a random walk over a potential minima with jump rates determined by the Arrhenius law. The averaged particle motion is found under the assumption of Gaussian distributions for characteristic properties of spatial heterogeneities.

Viscoelastic subdiffusion in a random Gaussian environment

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_BT, in the units of thermal energy), and strong (5-10k_BT) 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 compared 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.

Biased continuous-time random walks for ordinary and equilibrium cases: facilitation of diffusion, ergodicity breaking and ageing

We examine renewal processes with power-law waiting time distributions (WTDs) and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics. All possible values of the scaling exponent α are considered for the WTD ψ(t) ∼ 1/t1+α. We treat continuous-time random walks (CTRWs) with 0 < α < 1 for which the mean waiting time diverges, and investigate the behaviour of the process for both ordinary and equilibrium CTRWs for 1 < α < 2 and α > 2. We demonstrate that in the presence of a drift CTRWs with α < 1 are ageing and non-ergodic in the sense of the non-equivalence of their ensemble and time averaged displacement characteristics in the limit of lag times much shorter than the trajectory length. In the sense of the equivalence of ensemble and time averages, CTRW processes with 1 < α < 2 are ergodic for the equilibrium and non-ergodic for the ordinary situation. Lastly, CTRW renewal processes with α > 2-both for the equilibrium and ordinary situation-are always ergodic. For the situations 1 < α < 2 and α > 2 the variance of the diffusion process, however, depends on the initial ensemble. For biased CTRWs with α > 1 we also investigate the behaviour of the ergodicity breaking parameter. In addition, we demonstrate that for biased CTRWs the Einstein relation is valid on the level of the ensemble and time averaged displacements, in the entire range of the WTD exponent α.

Percolation thresholds and fractal dimensions for square and cubic lattices with long-range correlated defects

We study long-range power-law correlated disorder on square and cubic lattices. In particular, we present high-precision results for the percolation thresholds and the fractal dimension of the largest clusters as a function of the correlation strength. The correlations are generated using a discrete version of the Fourier filtering method. We consider two different metrics to set the length scales over which the correlations decay, showing that the percolation thresholds are highly sensitive to such system details. By contrast, we verify that the fractal dimension d_{f} is a universal quantity and unaffected by the choice of metric. We also show that for weak correlations, its value coincides with that for the uncorrelated system. In two dimensions we observe a clear increase of the fractal dimension with increasing correlation strength, approaching d_{f}→2. The onset of this change does not seem to be determined by the extended Harris criterion.