Solution of a class of one-dimensional reaction-diffusion models in disordered media

Details Solution of a class of one-dimensional reaction-diffusion models in disordered media Solution of a class of one-dimensional reaction-diffusion models in disordered media

2001-01-17

arxiv.org/abs/cond-mat/0101253v2

Physics

Condensed Matter

Statistical Mechanics

11 pages, no figures. To appear in Phys.Rev.B

Scientific paper

10.1103/PhysRevB.64.064203

We study a one-dimensional class of reaction-diffusion models on a $10-$parameters manifold. The equations of motion of the correlation functions close on this manifold. We compute exactly the long-time behaviour of the density and correlation functions for {\it quenched} disordered systems. The {\it quenched} disorder consists of disconnected domains of reaction. We first consider the case where the disorder comprizes a superposition, with different probabilistic weights, of finite segments, with {\it periodic boundary conditions}. We then pass to the case of finite segments with {\it open boundary conditions}: we solve the ordered dynamics on a open lattice with help of the Dynamical Matrix Ansatz (DMA) and investigate further its disordered version.

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