A parity breaking Ising chain Hamiltonian as a Brownian motor

Abstract

We consider the translationally invariant but parity (left-right symmetry) breaking Ising chain Hamiltonianand 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 = k s k . The symmetry of the U 3 term in the Hamiltonian is discussed.

Density decay and growth of correlations in the Game of Life

“…Bennett and Bourzutschky [17] obtain a correlation length of 42±3 lattice distances, which compares favorably with our ξ ∞ = 50 ± 10. Their value is based, essentially, on the penetration length of the density into the system away from a boundary of cells kept alive randomly; we have independently confirmed [26] the length obtained by such a procedure. The relaxation time of 200 ± 10 time steps reported by same authors [17] is an average time and refers to the relaxation of external perturbations; it cannot be compared to the asymptotic time τ ∞ of present work.…”