Why current flows: A multiparticle one-dimensional model

In all known microscopic models of electric current including the basic Drude model, charged particles are accelerated by an external force and some random environment retards them. We introduce a classical multiparticle deterministic one-dimensional model on an interval with nearest-neighbor interaction, explaining how current can flow if the external force acts only on the ends of the passive part (i.e., outside the generator, battery, etc.) of the conductor. We obtain a family of explicit solutions.