Unbiased diffusion of Brownian particles on disordered correlated potentials

2017

J. Stat. Mech.

We introduce a simple model of deterministic particles in weakly disordered media which exhibits a transition from normal to anomalous diffusion. The model consists of a set of non-interacting overdamped particles moving on a disordered potential. The disordered potential can be thought as a substrate having some "defects" scattered along a one-dimensional line. The distance between two contiguous defects is assumed to have a heavy-tailed distribution with a given exponent α, which means that the defects along the substrate are scarce if α is small. We prove that this system exhibits a transition from normal to anomalous diffusion when the distribution exponent α decreases, i.e., when the defects become scarcer. Thus we identify three distinct scenarios: a normal diffusive phase for α > 2, a superdiffusive phase for 1/2 < α ≤ 2, and a subdiffusive phase for α ≤ 1/2. We also prove that the particle current is finite for all the values of α, which means that the transport is normal independently of the diffusion regime (normal, subdiffusive, or superdiffusive). We give analytical expressions for the effective diffusion coefficient for the normal diffusive phase and analytical expressions for the diffusion exponent in the case of anomalous diffusion. We test all these predictions by means of numerical simulations.

Section: V(x)mentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

Scarce defects induce anomalous diffusion

Hidalgo-Soria

2017

J. Stat. Mech.

“…Then we use the particlepolymer model that has been studied in Refs. [8][9][10][11][12] to study the dynamics of Brownian particles on random potentials. Particularly we show that, under the influence of an unbiased time-dependent periodic forcing, the spatial irreversibility of the medium induces a rectification phenomenon similar to the one occurring in the so-called rocked thermal ratchets.…”

Section: Introductionmentioning

confidence: 99%

Noise-induced rectification in out-of-equilibrium structures

2019

Phys. Rev. E

We consider the motion of overdamped particles over random potentials subjected to a Gaussian white noise and a time-dependent periodic external forcing. The random potential is modeled as the potential resulting from the interaction of a point particle with a random polymer. The random polymer is made up, by means of some stochastic process, from a finite set of possible monomer types. The process is assumed to reach a non-equilibrium stationary state, which means that every realization of a random polymer can be considered as an out-of-equilibrium structure. We show that the net flux of particles over this random medium is non-vanishing when the potential profile on every monomer is symmetric. We prove that this ratchet-like phenomenon is a consequence of the irreversibility of the stochastic process generating the polymer. On the contrary, when the process generating the polymer is at equilibrium (thus fulfilling the detailed balance condition) the system is unable to rectify the motion. We calculate the net flux of the particles in the adiabatic limit for a simple model and we test our theoretical predictions by means of Langevin dynamics simulations. We also show that, out of the adiabatic limit, the system also exhibits current reversals as well as non-monotonic dependence of the diffusion coefficient as a function of forcing amplitude.

“…Depending on the model type, the system can exhibit normal or anomalous transport accompanied of normal or anomalous diffusion. For example, recent works have revealed that a system of overdamped particles on a random potential the unbiased diffusion is always normal independently of the correlations [3,4]. In contrast, in models with uncorrelated Gaussian random force field exhibit anomalous diffusion when the system is unbiased (i.e., when the system is not subjected to a constant driving force and consequently it does not exhibit net transport) [2,5,6].…”

Section: Introductionmentioning

confidence: 99%

Normal and anomalous diffusion of Brownian particles on disordered potentials

Physica A: Statistical Mechanics and its Applications

2016

In this work we study the transition from normal to anomalous diffusion of Brownian particles on disordered potentials. The potential model consists of a series of "potential hills" (defined on unit cell of constant length) whose heights are chosen randomly from a given distribution. We calculate the exact expression for the diffusion coefficient in the case of uncorrelated potentials for arbitrary distributions. We particularly show that when the potential heights have a Gaussian distribution (with zero mean and a finite variance) the diffusion of the particles is always normal. In contrast when the distribution of the potential heights are exponentially distributed we show that the diffusion coefficient vanishes when system is placed below a critical temperature. We calculate analytically the diffusion exponent for the anomalous (subdiffusive) phase by using the so-called "random trap model". We test our predictions by means of Langevin simulations obtaining good agreement within the accuracy of our numerical calculations.