A parity breaking Ising chain Hamiltonian as a Brownian motor

We consider the translationally invariant but parity (left-right symmetry) breaking Ising chain Hamiltonian and let this system evolve by Kawasaki spin exchange dynamics. Monte Carlo simulations show that perturbations forcing this system off equilibrium make it act as a Brownian molecular motor which, in the lattice gas interpretation, transports particles along the chain. We determine the particle current under various different circumstances, in particular as a function of the ratio and of the conserved magnetization . The symmetry of the U3 term in the Hamiltonian is discussed.