Energy-dependent diffusion in a soft periodic Lorentz gas
arXiv:1811.11661 · doi:10.1140/epjst/e2019-800136-8
Abstract
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.
arXiv comment16 pages, 13 figures
References in corpus (16)
- Engineering artificial graphene in a two-dimensional electron gas
- Simple Maps with Fractal Diffusion Coefficients
- Simple deterministic dynamical systems with fractal diffusion coefficients
- Chaotic and fractal properties of deterministic diffusion-reaction processes
- Survey on the role of accelerator modes for anomalous diffusion: The case of the standard map
- Density-dependent diffusion in the periodic Lorentz gas
- Electron-Electron Interactions in Artificial Graphene
- Understanding deterministic diffusion by correlated random walks
- Normal and Anomalous Diffusion in Soft Lorentz Gases
- Negative and Nonlinear Response in an Exactly Solved Dynamical Model of Particle Transport
- Global and Local diffusion in the Standard Map
- Deterministic diffusion in flower shape billiards
- Strong anomalous diffusion of the phase of a chaotic pendulum
- Transport properties of Lévy walks: an analysis in terms of multistate processes
- Bill2d - a software package for classical two-dimensional Hamiltonian systems
- On (in)elastic non-dissipative Lorentz gases and the (in)stability of classical pulsed and kicked rotors