https://doi.org/10.1140/epjst/e2019-800136-8
Regular Article
Energy-dependent diffusion in a soft periodic Lorentz gas
1
Queen Mary University of London, School of Mathematical Sciences,
Mile End Road,
London E1 4NS, UK
2
Institut für Theoretische Physik, Technische Universität Berlin,
Hardenbergstraße 36,
10623
Berlin, Germany
3
Institute for Theoretical Physics, University of Cologne,
Zülpicher Straße 77,
50937
Cologne, Germany
4
Computational Physics Laboratory, Tampere University,
P.O. Box 692,
33014
Tampere, Finland
a e-mail: s.gilgallegos@qmul.ac.uk
Received:
26
August
2018
Received in final form:
2
November
2018
Published online: 30 May 2019
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.
© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2019
