Exactly solvable deterministic lattice model of crossover between ballistic and diffusive transport

TL;DR

This paper presents an exactly solvable deterministic lattice model demonstrating coexistence of ballistic and diffusive transport, with analytical calculations of transport coefficients and dynamic properties.

Contribution

It introduces a simple deterministic lattice gas model with analytically computed transport coefficients and exact solutions for dynamic structure factor and quench problems.

Findings

Coexistence of ballistic and diffusive transport in the model

Analytical expressions for Drude weight and diffusion constant

Exact solutions for dynamic structure factor and inhomogeneous quench

Abstract

We discuss a simple deterministic lattice gas of locally interacting charged particles, for which we show coexistence of ballistic and diffusive transport. Both, the ballistic and the diffusive transport coefficients, specifically the Drude weight and the diffusion constant, respectively, are analytically computed for particular set of generalised Gibbs states and may independently vanish for appropriate values of thermodynamic parameters. Moreover, our analysis, based on explicit construction of the matrix representation of time-automorphism in a suitable basis of the algebra of local observables, allows for an exact computation of the dynamic structure factor and closed form solution of the inhomogeneous quench problem.