Work

Particle transport and finite-size effects in Lorentz channels with finite horizons

Year: 2024

Type: article

Abstract: Particle transport is investigated in a finite-size realization of the classical Lorentz gas model. We consider point particles moving at constant speed in a 2D rectangular strip of finite length, filled with circular scatterers sitting at the vertices of a triangular lattice. Particles are injected at the left boundary with a prescribed rate, undergo specular reflections when colliding with the scatterers and the horizontal boundaries of the channel, and are finally absorbed at the left or the right boundary. Thanks to the equivalence with give Correlated Random Walks , in the finite horizon case, we show that the inverse probability that a particle exits through the right boundary depends linearly on the number of cells in the channel. A non-monotonic behavior of such probability as a function of the density of scatterers is also discussed and traced back analytically to the geometric features of a single trap. This way, we do not refer to asymptotic quantities and we accurately quantify the finite size effects. Our deterministic model provides a microscopic support for a variety of phenomenological laws, e.g. the Darcy’s law for porous media and the Ohm’s law in electronic transport.

Source: Physica D Nonlinear Phenomena

DOI: 10.1016/j.physd.2024.134512

Authors: Emilio N.M. Cirillo, Matteo Colangeli, Martin Kröger, Lamberto Rondoni

Institutions: Sapienza University of Rome, University of L'Aquila, ETH Zurich, Politecnico di Torino, Istituto Nazionale di Fisica Nucleare, Sezione di Torino

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,370