Related papers: Normal diffusion in crystal structures and higher-…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
The problem of the lattice diffusion of two particles coupled by a contact repulsive interaction is solved by finding analytical expressions of the two-body probability characteristic function. The interaction induces anomalous drift with a…
Percolation on a one-dimensional lattice and fractals such as the Sierpinski gasket is typically considered to be trivial because they percolate only at full bond density. By dressing up such lattices with small-world bonds, a novel…
For a better understanding of the chaotic behavior of systems of many moving particles it is useful to look at other systems with many degrees of freedom. An interesting example is the high-dimensional Lorentz gas, which, just like a system…
We construct Birkhoff cones for dispersing billiards, which are contracted by the action of the transfer operator. This construction permits the study of statistical properties not only of regular dispersing billiards but also of sequential…
Transport by normal diffusion can be decomposed into the so-called hydrodynamic modes which relax exponentially toward the equilibrium state. In chaotic systems with two degrees of freedom, the fine scale structure of these hydrodynamic…
The properties of a particle diffusing on a one-dimensional lattice where at each site a random barrier and a random trap act simultaneously on the particle are investigated by numerical and analytical techniques. The combined effect of…
The problem of two interacting particles moving in a d-dimensional billiard is considered here. A suitable coordinate transformation leads to the problem of a particle in an unconventional hyperbilliard. A dynamical map can be readily…
We study a system of particles which jump on the sites of the interval $[1,L]$ of $\mathbb Z$. The density at the boundaries is kept fixed to simulate the action of mass reservoirs. The evolution depends on two parameters $\lambda'\ge 0$…
In this paper we investigate deterministic diffusion in systems which are spatially extended in certain directions but are restricted in size and open in other directions, consequently particles can escape. We introduce besides the…
Past work has shown that ions can pass through a membrane more readily in one direction than the other. We demonstrate here in a model and an experiment that for a mixture of small and large particles such asymmetric diffusion can arise…
Motivated by the mean field prediction of a Gardner phase transition between a "normal glass" and a "marginally stable glass", we investigate the off-equilibrium dynamics of three-dimensional polydisperse hard spheres, used as a model for…
The spontaneous symmetry breaking in a vibro-fluidized low-density granular gas in three connected compartments is investigated. When the total number of particles in the system becomes large enough, particles distribute themselves…
We review a virial-type estimate which bounds the strength of interaction for a gas of $N$ hard spheres (billiard balls) dispersing into Euclidean space $\mathbb{R}^d$. This type of estimate has been known for decades in the context of…
We analyze diffusion of small particles in a solid polymeric medium taking into account a short range particle-polymer interaction. The system is modeled by a particle diffusion on a ternary lattice where the sites occupied by polymer…
How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder…
We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the…
Have you ever played or watched a game of pool? If so, you have already seen a billiard system in action. In mathematics and physics, a billiard system describes a ball that moves in straight lines and bounces off walls. Despite these…
Boundary-induced transport in particle systems with anomalous diffusion exhibits rectification, negative resistance, and hysteresis phenomena depending on the way the drive acts on the boundary. The solvable case of a 1D system…
Polygonal billiards constitute a special class of models. Though they have zero Lyapunov exponent their classical and quantum properties are involved due to scattering on singular vertices. It is demonstrated that in the semiclassical limit…