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Prompted by recent experimental developments, a theory of surface scattering of fast atoms at grazing incidence is developed. The theory gives rise to a quantum mechanical limit for ordered surfaces that describes coherent diffraction peaks…
It was recently proposed to use extra-galactic point sources to constrain space-time quantum fluctuations in the universe. In these proposals, the fundamental "fuzziness" of distance caused by space-time quantum fluctuations have been…
We study the diffusive behavior of biased Brownian particles in a two dimensional confined geometry filled with the freezing obstacles. The transport properties of these particles are investigated for various values of the obstacles density…
We study the limiting behaviour of the empirical measure of a system of diffusions interacting through their ranks when the number of diffusions tends to infinity. We prove that the limiting dynamics is given by a McKean-Vlasov evolution…
We compare experiments and direct numerical simulations to evaluate the accuracy of the Stokes-drag model, which is used widely in studies of inertial particles in turbulence. We focus on statistics at the dissipation scale and on extreme…
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…
Though classical random walks have been studied for many years, research concerning their quantum analogues, quantum random walks, has only come about recently. Numerous simulations of both types of walks have been run and analyzed, and are…
We generalize Einstein's master equation for random walk processes by considering that the probability for a particle at position $r$ to make a jump of length $j$ lattice sites, $P_j(r)$ is a functional of the particle distribution function…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
The two--dimensional diffusive dynamics of test particles in a random electromagnetic field is studied. The synthetic electromagnetic fluctuations are generated through randomly placed magnetised ``clouds'' oscillating with a frequency…
We analyse diffusion at low temperature by bringing the fluctuation-dissipation theorem (FDT) to bear on a physically natural, viscous response-function R(t). The resulting diffusion-law exhibits several distinct regimes of time and…
The ensemble properties and time-averaged observables of a memory-induced diffusive-superdiffusive transition are studied. The model consists in a random walker whose transitions in a given direction depend on a weighted linear combination…
A conditional diffusion model has been developed to analyze intricate conductance fluctuations called universal conductance fluctuations or quantum fingerprints appearing in quantum transport phenomena. The model reconstructs impurity…
We investigate the diffusive motion of an overdamped classical particle in a 1D random potential using the mean first-passage time formalism and demonstrate the efficiency of this method in the investigation of the large-time dynamics of…
We formulate the generalized master equation for a class of continuous time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an…
It is shown that the characteristics of the mesoscopic fluctuations in the conventional quantum-diffusion model and the model of the non-coherent (`classical') diffusion in media with long-range correlated disorder are quite similar in the…
Random walks in random environments (RWRE) model transport in quenched disorder, incorporating spatial heterogeneity, trapping, random drift, and random geometry. This paper summarizes discrete and continuous time formulations, identifies…
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…
We present a random-matrix realization of a two-dimensional percolation model with the occupation probability $p$. We find that the behavior of the model is governed by the two first extreme eigenvalues. While the second extreme eigenvalue…