Diffusion in the Inverted Triangular Soft Lorentz Gas

TL;DR

This paper studies diffusion in a two-dimensional inverted soft Lorentz gas with attractive potential wells arranged in a triangular lattice, revealing complex behaviors and developing an extended theoretical model.

Contribution

It introduces the first systematic analysis of diffusion in inverted soft Lorentz gases and extends the Machta-Zwanzig approximation to account for correlated trajectories and localized orbits.

Findings

Identification of tongue-like structures in parameter space indicating quasiballistic transport

Development of an extended Machta-Zwanzig approximation incorporating correlations

Demonstration of qualitative and quantitative differences from repulsive Lorentz gases

Abstract

We investigate diffusion in a two-dimensional inverted soft Lorentz gas, where attractive Fermi-type potential wells are arranged in a triangular lattice. This configuration contrasts with earlier studies of soft Lorentz gases involving repulsive scatterers. By systematically varying the gap width and softness of the potential, we explore a rich landscape of diffusive behaviors. We present numerical simulations of the mean squared displacement and compute diffusion coefficients, identifying tongue-like structures in parameter space associated with quasiballistic transport. Furthermore, we develop an extension to the Machta-Zwanzig approximation that incorporates correlated multi-hop trajectories and correct for the influence of localized periodic orbits. Our findings highlight the qualitative and quantitative differences between inverted and repulsive soft Lorentz gases and offer new insights into transport phenomena in smooth periodic potentials.