A parity breaking Ising chain Hamiltonian as a Brownian motor

TL;DR

This paper investigates a parity-breaking Ising chain Hamiltonian that, when driven out of equilibrium, functions as a Brownian motor, transporting particles along the chain with properties dependent on system parameters.

Contribution

It introduces a novel parity-breaking Hamiltonian and demonstrates its ability to act as a Brownian motor under non-equilibrium conditions, with detailed analysis of particle current behavior.

Findings

The system acts as a Brownian motor under perturbations.

Particle current depends on the ratio U_3/U_2.

Current varies with conserved magnetization M.

Abstract

We consider the translationally invariant but parity (left-right symmetry) breaking Ising chain Hamiltonian \begin{equation} {\cal H} = -U_2\sum_{k} s_{k}s_{k+1} - U_3\sum_{k} s_{k}s_{k+1}s_{k+3} \nonumber \end{equation} 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 $U_3/U_2$ and of the conserved magnetization $M=\sum_k s_k$. The symmetry of the $U_3$ term in the Hamiltonian is discussed