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The Lorentz gas, a point particle making mirror-like reflections from an extended collection of scatterers, has been a useful model of deterministic diffusion and related statistical properties for over a century. This survey summarises recent results, including periodic and aperiodic models, finite and infinite horizon, external fields, smooth or polygonal obstacles, and in the Boltzmann-Grad limit. New results are given for several moving particles and for obstacles with flat points. Finally, a variety of applications are presented.
Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in time. Wha
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 particle wit
This paper presents an {it ab initio} derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class are Lorentz gases, where non-interacting particle
This is an easy-to-read introduction to foundations of deterministic chaos, deterministic diffusion and anomalous diffusion. The first part introduces to deterministic chaos in one-dimensional maps in form of Ljapunov exponents and dynamical entropie
In this paper we study the breakdown of normal hyperbolicity and its consequences for reaction dynamics; in particular, the dividing surface, the flux through the dividing surface (DS), and the gap time distribution. Our approach is to study these qu