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

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 a particular set of generalized 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.