Energy-dependent diffusion in a soft periodic Lorentz gas

• Published in: The European physical journal. ST, Special topics Vol. 228; no. 1; pp. 143 - 160
• Main Authors: Gil-Gallegos, S., Klages, R., Solanpää, J., Räsänen, E.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-05-2019; Springer Nature B.V
• Subjects: Atomic; Chaos and Transport in Nonequilibrium Processes; Classical and Continuum Physics; Computer simulation; Condensed Matter Physics; Diffusion; Diffusion coefficient; Electron transport; Graphene; Lorentz gas; Materials Science; Mathematical analysis; Measurement Science and Instrumentation; Microscopic Dynamics; Molecular; Optical and Plasma Physics; Physics; Physics and Astronomy; Random walk; Regular Article
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjst/e2019-800136-8

The periodic Lorentz gas is a paradigmatic model to examine how macroscopic transport emerges from microscopic chaos. It consists of a triangular lattice of circular hard scatterers with a moving point particle. Recently this system became relevant as a model for electronic transport in low-dimensional nanosystems such as molecular graphene. However, to more realistically mimic such dynamics, the hard Lorentz gas scatterers should be replaced by soft potentials. Here we study diffusion in a soft Lorentz gas with Fermi potentials under variation of the total energy of the moving particle. Our goal is to understand the diffusion coefficient as a function of the energy. In our numerical simulations we identify three different dynamical regimes: (i) the onset of diffusion at small energies; (ii) a transition where for the first time a particle reaches the top of the potential, characterized by the diffusion coefficient abruptly dropping to zero; and (iii) diffusion at high energies, where the diffusion coefficient increases according to a power law in the energy. All these different regimes are understood analytically in terms of simple random walk approximations.