Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAnomalous diffusion in random dynamical systems
77
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in time. What type of diffusion is exhibited by this {em random dynamical system}? We show that the resulting dynamics can generate anomalous diffusion, where in contrast to Brownian normal diffusion the mean square displacement of an ensemble of particles increases nonlinearly in time. Randomly mixing simple deterministic walks on the line we find anomalous dynamics characterised by ageing, weak ergodicity breaking, breaking of self-averaging and infinite invariant densities. This result holds for general types of noise and for perturbing nonlinear dynamics in bifurcation scenarios.
rate research
Read More
This is an easy-to-read introduction to foundations of deterministic chaos, deterministic diffusion and anomalous diffusion. The first part introduces to deterministic chaos in one-dimensional maps in form of Ljapunov exponents and dynamical entropies. The second part outlines the concept of deterministic diffusion. Then the escape rate formalism for deterministic diffusion, which expresses the diffusion coefficient in terms of the above two chaos quantities, is worked out for a simple map. Part three explains basics of anomalous diffusion by demonstrating the stochastic approach of continuous time random walk theory for an intermittent map. As an example of experimental applications, the anomalous dynamics of biological cell migration is discussed.
This paper presents an {it ab initio} derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class are Lorentz gases, where non-interacting particles move on a spatially periodic lattice, and collide elastically with fixed scatterers. The second class are periodic systems where $N$ particles interact with each other, and one of them is a tracer particle which diffuses among the cells of the lattice. We assume that, in either case, the dynamics of the system is deterministic and hyperbolic, with positive Lyapunov exponents. This work extends methods originally developed for a chaotic two-dimensional model of diffusion, the multi-baker map, to higher dimensional, continuous time dynamical systems appropriate for systems with one or more moving particles. Here we express the rate of entropy production in terms of hydrodynamic measures that are determined by the fractal properties of microscopic hydrodynamic modes that describe the slowest decay of the system to an equilibrium state.
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a dynamical phase transition from normal to anomalous diffusion marked by strong suppression of diffusion. Similarly, the probability density of moving particles is governed by a time-fractional diffusion equation on coarse scales while exhibiting a specific fine structure. Approximations beyond stochastic theory are derived from a generalized Taylor-Green-Kubo formula.
In this work we probe the dynamics of the particle-hole symmetric many-body localized (MBL) phase. We provide numerical evidence that it can be characterized by an algebraic propagation of both entanglement and charge, unlike in the conventional MBL case. We explain the mechanism of this anomalous diffusion through a formation of bound states, which coherently propagate via long-range resonances. By projecting onto the two-particle sector of the particle-hole symmetric model, we show that the formation and observed subdiffusive dynamics is a consequence of an interplay between symmetry and interactions.
The Lorentz gas, a point particle making mirror-like reflections from an extended collection of scatterers, has been a useful model of deterministic diffusion and related statistical properties for over a century. This survey summarises recent results, including periodic and aperiodic models, finite and infinite horizon, external fields, smooth or polygonal obstacles, and in the Boltzmann-Grad limit. New results are given for several moving particles and for obstacles with flat points. Finally, a variety of applications are presented.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
