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We discuss a simple deterministic lattice gas of locally interacting chargedparticles, for which we show coexistence of ballistic and diffusive transport.Both, the ballistic and the diffusive transport coefficients, specifically theDrude weight and the diffusion constant, respectively, are analyticallycomputed for particular set of generalised Gibbs states and may independentlyvanish for appropriate values of thermodynamic parameters. Moreover, ouranalysis, based on explicit construction of the matrix representation oftime-automorphism in a suitable basis of the algebra of local observables,allows for an exact computation of the dynamic structure factor and closed formsolution of the inhomogeneous quench problem.

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