Related papers: L\'evy walks on lattices as multi-state processes
We investigate multiple scattering of near-resonant light in a Doppler-broadened atomic vapor. We experimentally characterize the length distribution of the steps between successive scattering events. The obtained power law is…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
We study the ballistic L\'evy walk stemming from an infinite mean traveling time between collision events. Our study focuses on the density of spreading particles all starting from a common origin, which is limited by a `light' cone $-v_0…
In classical diffusion, particle step-sizes have a Gaussian distribution. However, in superdiffusion, they have power-law tails, with transport dominated by rare, long L\'evy flights. Similarly, if the time interval between scattering…
We study the transmission of random walkers through a finite-size inhomogeneous material with a quenched, long-range correlated distribution of scatterers. We focus on a finite one-dimensional structure where walkers undergo random…
The common perception is that strong coupling to the environment will always render the evolution of the system density matrix quasi-classical (in fact, diffusive) in the long time limit. We present here a counter-example, in which a…
We introduce a L\'evy-Lorentz gas in which a light particle is scattered by static point scatterers arranged on a line. We investigate the case where the intervals between scatterers $\{\xi_i \}$ are independent random variables identically…
We consider a continuous-time random walk which is defined as an interpolation of a random walk on a point process on the real line. The distances between neighboring points of the point process are i.i.d. random variables in the normal…
Many disordered systems show a superdiffusive dynamics, intermediate between the diffusive one, typical of a classical stochastic process, and the so called ballistic behaviour, which is generally expected for the spreading in a quantum…
Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…
L\'{e}vy walk is a popular and more `physical' model to describe the phenomena of superdiffusion, because of its finite velocity. The movements of particles are under the influences of external potentials almost at anytime and anywhere. In…
We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo…
The diffusive epidemic process is a paradigmatic example of an absorbing state phase transition in which healthy and infected individuals spread with different diffusion constants. Using stochastic activity spreading simulations in…
Properties of random and fluctuating systems are often studied through the use of Gaussian distributions. However, in a number of situations, rare events have drastic consequences, which can not be explained by Gaussian statistics.…
We study specific properties of particles transport by exploring an exact solvable model, a so-called comb structure, where diffusive transport of particles leads to subdiffusion. A performance of L\'evy -- like process enriches this…
We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…
The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different L\'evy processes: in the first model we…
Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…
We consider correlated L\'evy walks on a class of two- and three-dimensional deterministic self-similar structures, with correlation between steps induced by the geometrical distribution of regions, featuring different diffusion properties.…
Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random walk model with long range memory for which not only the mean square displacement (MSD) can be obtained exactly in the…