Related papers: Random and deterministic walks on lattices
The random walk of photons in a tight-binding lattice is known to exhibit diffusive motion similar to classical random walks under decoherence, clearly illustrating the quantum-to-classical transition. In this study, we reveal that the…
Random walks behave very differently for classical and quantum particles. Here we unveil a ubiquitous distinctive behavior of random walks of a photon in a one-dimensional lattice in the presence of a finite number of traps, at which the…
Simple random walks on various types of partially horizontally oriented regular lattices are considered. The horizontal orientations of the lattices can be of various types (deterministic or random) and depending on the nature of the…
Consider a randomly-oriented two dimensional Manhattan lattice where each horizontal line and each vertical line is assigned, once and for all, a random direction by flipping independent and identically distributed coins. A deterministic…
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on…
Two-dimensional networks of ordered quantum dots beyond the percolation threshold are studied, as typical example of conducting nanostructures with quenched random disorder. Theory predicts anomalous diffusion with stretched-exponential…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
The diffusive transport of particles in anisotropic media is a fundamental phenomenon in computational, medical and biological disciplines. While deterministic models (partial differential equations) of such processes are well established,…
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
We examine a very simple conceptual model of stochastic behavior based on a random walk process in velocity space. For objects engaged in classical non-relativistic velocities, this leads under asymmetric conditions to acceleration…
The dynamics of a discrete-time quantum walk (DTQW) can be realized within a purely classical interacting particle system composed of some boxes and a large but finite number of balls, and can, in principle, be implemented in a tabletop…
This note describes recent results on the localization properties of Random Quantum Walks on the d-dimensional lattice in a regime analogous to the large disorder regime by means of the Fractional Moments Method adapted to the unitary…
A one-dimensional driven diffusive system with two types of particles and nearest neighbors interactions has been considered on a finite lattice with open boundaries. The particles can enter and leave the system from both ends of the…
The classical walking behaviors of a single atom in an amplitude-modulated standing wave lattice beyond the internal dynamics are investigated. Based on a simple effective model, we identify a diversity of dynamic regimes of atomic motion…
We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation probability of an arbitrary site on the…
Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the…
Locally activated random walks are defined as random processes, whose dynamical parameters are modified upon visits to given activation sites. Such dynamics naturally emerge in living systems as varied as immune and cancer cells interacting…
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…