Single-Species Reactions on a Random Catalytic Chain

Abstract

We present an exact solution for a catalytically-activated annihilation A + A \to 0 reaction taking place on a one-dimensional chain in which some segments (placed at random, with mean concentration p) possess special, catalytic properties. Annihilation reaction takes place, as soon as any two A particles land from the reservoir onto two vacant sites at the extremities of the catalytic segment, or when any A particle lands onto a vacant site on a catalytic segment while the site at the other extremity of this segment is already occupied by another A particle. We find that the disorder-average pressure $P^{(quen)}$ per site of such a chain is given by $P^{(quen)}=P^{(lan)}+{\beta }^{-1}F$, where $P^{(lan)}={\beta }^{-1}\ln (1+z)$ is the Langmuir adsorption pressure, (z being the activity and β^{-1} - the temperature), while ${\beta }^{-1}F$ is the reaction-induced contribution, which can be expressed, under appropriate change of notations, as the Lyapunov exponent for the product of 2 \times 2 random matrices, obtained exactly by Derrida and Hilhorst (J. Phys. A {\bf 16}, 2641 (1983)). Explicit asymptotic formulae for the particle mean density and the compressibility are also presented.

AMSTeX, 17 pages, 1 figure, submitted to J. Phys. A

References in corpus (2)

• Random Fibonacci Sequences
• On the Reactions A+A+...+A->0 at a One-Dimensional Periodic Lattice of Catalytic Centers: Exact Solution

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• A generating function approach to the growth rate of random matrix products