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We present an extensive analysis of transport properties in superdiffusive two dimensional quenched random media, obtained by packing disks with radii distributed according to a L\'evy law. We consider transport and scaling properties in…
The statistics of charge transport across a tunnel junction with energy-dependent scattering is investigated. A model with quadratic dispersion relation is discussed in general and, independently, in the two limiting cases of a large…
We study the dynamics of condensation for a stochastic continuous mass transport process defined on a one-dimensional lattice. Specifically we introduce three different variations of the truncated random average process. We generalize…
A relation derived from the Kubo formula shows that optical conductivity measurements below the gap frequency in doped semiconductors can be used to probe directly the time-dependent quantum dynamics of charge carriers. This allows to…
We study transport in a model perturbed integrable Hamiltonian system by calculating the volume, V(t), of elementary phase space cells visited by a trajectory, as a function of time. We use this function in order to "measure" the fractality…
From Liouville's equation, a phase-space multi-scale transport equation is systematically derived. The proposed phase-space multi-scale transport equation based on the first principle indicates that the nonlinear stochastic transport is due…
A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a…
The statistical properties of the conductance of one dimensional disordered systems are studied at finite bias voltage V and temperature T, in an independent-electron picture. We calculate the complete distribution of the conductance P(G)…
We study anomalous transport arising in disordered one-dimensional spin chains, specifically focusing on the subdiffusive transport typically found in a phase preceding the many-body localization transition. Different types of transport can…
We report a new result concerning the dynamics of an initially localized wave packet in quantum nonlinear Schr\"odinger lattices with a disordered potential. A class of nonlinear lattices with subquadratic power nonlinearity is considered.…
The peculiarities of electric current in semiconductors with nonuniform distribution of charge carriers are studied. The semiclassical drift-diffusion equations consisting of the continuity equations and the Poisson equation are solved…
Waiting time is an important transport quantity that is complementary to average current and its fluctuation. So far all the studies of waiting time distribution (WTD) are limited to steady state transport (either dc or ac). In this work,…
We have studied the Waiting Time Distributions (WTDs) for sub-gap transport through a single-level quantum dot tunnel coupled to one normal and one superconducting lead. The WTDs reveal the internal dynamics of the system in particular the…
We present the results of a numerical investigation of charged-particle transport across a synthesized magnetic configuration composed of a constant homogeneous background field and a multiscale perturbation component simulating an effect…
We investigate the transport of a passive tracer in a two-dimensional stratified random medium with flow parallel and perpendicular to the strata. Assuming a Gaussian random flow with a Gaussian correlation function, it is not only possible…
A new method is developed for the study of transport properties of 1D models with random potentials. It is based on an exact transformation that reduces discrete Schr\"odinger equation in the tight-binding model to a two-dimensional…
In this review, we provide an account of the recent progress in understanding electronic transport in disordered graphene systems. Starting from a theoretical description that emphasizes the role played by band structure properties and…
Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be…
Multi-scaling properties of one-dimensional truncated Levy flights are studied. Due to the broken self-similarity of the distribution of jumps, they are expected to possess multi-scaling properties in contrast to the ordinary Levy flights.…
Transport phenomena are ubiquitous in nature and known to be important for various scientific domains. Examples can be found in physics, electrochemistry, heterogeneous catalysis, physiology, etc. To obtain new information about diffusive…