Related papers: Periodic One-Dimensional Hopping Model with one Mo…
We scrutinize the anomalies in diffusion observed in an extended long-range system of classical rotors, the HMF model. Under suitable preparation, the system falls into long-lived quasi-stationary states presenting super-diffusion of rotor…
The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
This work examines a mobile impurity interacting with a bath of a few spin-$\uparrow$ and spin-$\downarrow$ fermions in a small one-dimensional open lattice system. We study ground-state properties using the exact diagonalization method,…
Persistent random walks are intermediate transport processes between a uniform rectilinear motion and a Brownian motion. They are formed by successive steps of random finite lengths and directions travelled at a fixed speed. The isotropic…
Chemical master equation plays an important role to describe the time evolution of homogeneous chemical system. In addition to the reaction process, it is also accompanied by physical diffusion of the reactants in complex system that is…
We study quantum transport properties of finite periodic quasi-one-dimensional waveguides whose classical dynamics is diffusive. The system we consider is a scattering configuration, composed of a finite periodic chain of $L$ identical…
We examine the bound state(s) associated with a single cubic nonlinear impurity, in a one-dimensional tight-binding lattice, where hopping to first--and--second nearest neighbors is allowed. The model is solved in closed form {\em v\`{\i}a}…
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…
For certain materials science scenarios arising in rubber technology, one-dimensional moving boundary problems (MBPs) with kinetic boundary conditions are capable of unveiling the large-time behavior of the diffusants penetration front,…
We propose using an equation-of-motion approach as an impurity solver for dynamical mean field theory. As an illustration of this technique, we consider a finite-$U$ Hubbard model defined on the Bethe lattice with infinite connectivity at…
We study general linear transport-reaction systems on an arbitrary dimensional hypercube with periodic boundary conditions. Transport-reaction systems are often used to model the finite speed movement and interaction of particles, bacteria…
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…
As the simplest non-Fermi liquids, orthogonal metals have gapped single-particle excitations but show normal metallic behaviors in thermodynamic and transport quantities. Such an exotic metallic state could be realized in a Hubbard model…
In this paper we present analytical and random walk based solutions to diffusion in semi-permeable layered media with varying diffusivity. We propose a new random walk transit model (hybrid model) based on treating the membrane permeability…
In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out…
Active walker models have proved to be extremely effective in understanding the evolution of a large class of systems in biology like ant trail formation and pedestrian trails. We propose a simple model of a random walker which modifies its…
Stationary states of random walks with finite induced drift velocity on one-dimensional lattices with aperiodic disorder are investigated by scaling analysis. Three aperiodic sequences, the Thue-Morse (TM), the paperfolding (PF), and the…
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…
Randomly breaking connections in a graph alters its transport properties, a model used to describe percolation. In the case of quantum walks, dynamic percolation graphs represent a special type of imperfections, where the connections appear…