Exact dynamics of a reaction-diffusion model with spatially alternating rates

Details Exact dynamics of a reaction-diffusion model with spatially alternating rates Exact dynamics of a reaction-diffusion model with spatially alternating rates

2004-12-21

arxiv.org/abs/cond-mat/0412576v3

Phys. Rev. E 71, 056129 (2005)

Physics

Condensed Matter

Statistical Mechanics

13 pages, 1 table, revtex4 format (few minor typos fixed). Published in Physical Review E

Scientific paper

10.1103/PhysRevE.71.056129

We present the exact solution for the full dynamics of a nonequilibrium spin chain and its dual reaction-diffusion model, for arbitrary initial conditions. The spin chain is driven out of equilibrium by coupling alternating spins to two thermal baths at different temperatures. In the reaction-diffusion model, this translates into spatially alternating rates for particle creation and annihilation, and even negative ``temperatures'' have a perfectly natural interpretation. Observables of interest include the magnetization, the particle density, and all correlation functions for both models. Two generic types of time-dependence are found: if both temperatures are positive, the magnetization, density and correlation functions decay exponentially to their steady-state values. In contrast, if one of the temperatures is negative, damped oscillations are observed in all quantities. They can be traced to a subtle competition of pair creation and annihilation on the two sublattices. We comment on the limitations of mean-field theory and propose an experimental realization of our model in certain conjugated polymers and linear chain compounds.

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