Related papers: Crossover from Diffusive to Ballistic Transport in…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…
Quantum walks are quantum counterparts of random walks and their probability distributions are different from each other. A quantum walker distributes on a Hilbert space and it is observed at a location with a probability. The finding…
We present a theoretical and numerical study of the competition between two opposite interference effects, namely interference-induced ballistic transport on one hand, and strong (Anderson) localization on the other. While the former effect…
Conventional transport theory focuses on either the diffusive or ballistic regimes and neglects the crossover region between the two. In the presence of spin-orbit coupling, the transport equations are known only in the diffusive regime,…
Generic 2D Hamiltonian systems possess partial barriers in their chaotic phase space that restrict classical transport. Quantum mechanically the transport is suppressed if Planck's constant h is large compared to the classical flux, h >>…
Systems are studied in which transport is possible due to large extension with open boundaries in certain directions but the particles responsible for transport can disappear from it by leaving it in other directions, by chemical reaction…
We study the dynamics of a single-particle wave packet on a one-dimensional lattice subject to periodic random phase kicks with finite spatial correlation length. This stroboscopic setting provides a controllable model of dephasing in…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
In this work, surface diffusion is studied with a different perspective by showing how the corresponding open dynamics is transformed when passing, in a continuous and smooth way, from a pure quantum regime to a full classical regime; the…
We propose a stochastic model for intracellular transport processes associated with the activity of molecular motors. This out-of-equilibrium model, based on a generalized Langevin equation, considers a particle immersed in a viscoelastic…
In the classical transport theory, the coefficients such as the diffusion, thermal conductivity and viscosity of fluid are usually expressed in a form proportional to the mean free path of molecules. We point out that this may cause a great…
We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…
We study the dynamics of a generalization of quantum coin walk on the line which is a natural model for a diffusion modified by quantum or interference effects. In particular, our results provide surprisingly simple explanations to…
One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…
We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…
We discuss spreading estimates for dynamical systems given by the iteration of an extended CMV matrix. Using a connection due to Cantero--Gr\"unbaum--Moral--Vel\'azquez, this enables us to study spreading rates for quantum walks in one…
We consider supercritical branching random walks on transitive graphs and we prove a law of large numbers for the mean displacement of the ensemble of particles, and a Stam-type central limit theorem for the empirical distributions, thus…
Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker,…
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…
We investigate the dynamics of non-interacting particles in a one-dimensional tight-binding chain in the presence of an electric field with random amplitude drawn from a Gaussian distribution, and explicitly focus on the nature of quantum…