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Single-Species Reactions on a Random Catalytic Chain | | G.Oshanin
; S.F.Burlatsky
; | | Date: |
28 Sep 2002 | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Affiliation: | LPTL, University of Paris 6, France; UTRC, East Hartford, CT USA | | Abstract: | We present an exact solution for a catalytically-activated annihilation A + A o 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 $P^{(quen)} = P^{(lan)} + eta^{-1} F$, where $P^{(lan)} = eta^{-1} ln(1+z)$ is the Langmuir adsorption pressure, (z being the activity and eta^{-1} - the temperature), while $eta^{-1} F$ is the reaction-induced contribution, which can be expressed, under appropriate change of notations, as the Lyapunov exponent for the product of 2 imes 2 random matrices, obtained exactly by Derrida and Hilhorst (J. Phys. A {f 16}, 2641 (1983)). Explicit asymptotic formulae for the particle mean density and the compressibility are also presented. | | Source: | arXiv, cond-mat/0209656 | | Services: | Forum | Review | PDF | Favorites | |
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