The Lorentz Gas

19 - 23 December 2022

Venue: Lorentz Center@Oort

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The Lorentz gas is an idealized model of a solid proposed in 1905 by H.A. Lorentz to describe the thermal and electrical properties of metals (like iron). The nuclei of the atoms of the metal form a rectangular grid and the electrons move freely between them (as if they were part of an infinite pinball machine). A periodic Lorentz gas consists of unit mass particles moving and bouncing in a periodic grid of scatterers. The statistical properties of the spread (or diffusion) of the electrons through the grid remains a topic of interest to this day, because it determines the thermal and electrical conductivity of the metal.

 The goal of the workshop is to bring together researchers from three areas: ergodic theory, statistical
physics, probability theory. Concrete aims are:

 (A) Discuss the most recent strategies to tackle the problem of proving mixing for the periodic Lorentz
gas. This includes the employment of proper tools to deal with Hamiltonian and stochastic systems that have strong space-time dependencies.

 (B) Discuss challenging models such as the non-periodic Lorentz gas and the random Lorentz gas, with the aim of looking for simplifying assumptions that allow techniques developed for the periodic Lorentz gas to be carried over.

 (C) Discuss recent advances in probabilistic modelling of particle motion, especially within the theory of random walks with random transition kernels, referred to as Random Walks in Random Environments (RWREs). These can lead to fresh ideas and new techniques in the study of non-periodic and random Lorentz gases.


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