2,362 research outputs found

    Asymptotic expansion for reversible A + B <-> C reaction-diffusion process

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    We study long-time properties of reversible reaction-diffusion systems of type A + B C by means of perturbation expansion in powers of 1/t (inverse of time). For the case of equal diffusion coefficients we present exact formulas for the asymptotic forms of reactant concentrations and a complete, recursive expression for an arbitrary term of the expansions. Taking an appropriate limit we show that by studying reversible reactions one can obtain "singular" solutions typical of irreversible reactions.Comment: 6 pages, no figures, to appear in PR

    Localization-delocalization transition of a reaction-diffusion front near a semipermeable wall

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    The A+B --> C reaction-diffusion process is studied in a system where the reagents are separated by a semipermeable wall. We use reaction-diffusion equations to describe the process and to derive a scaling description for the long-time behavior of the reaction front. Furthermore, we show that a critical localization-delocalization transition takes place as a control parameter which depends on the initial densities and on the diffusion constants is varied. The transition is between a reaction front of finite width that is localized at the wall and a front which is detached and moves away from the wall. At the critical point, the reaction front remains at the wall but its width diverges with time [as t^(1/6) in mean-field approximation].Comment: 7 pages, PS fil

    Diffusion-Limited Annihilation with Initially Separated Reactants

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    A diffusion-limited annihilation process, A+B->0, with species initially separated in space is investigated. A heuristic argument suggests the form of the reaction rate in dimensions less or equal to the upper critical dimension dc=2d_c=2. Using this reaction rate we find that the width of the reaction front grows as t1/4t^{1/4} in one dimension and as t1/6(lnt)1/3t^{1/6}(\ln t)^{1/3} in two dimensions.Comment: 9 pages, Plain Te

    Kondo lattice model with a direct exchange interaction between localized moments

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    We study the Kondo lattice model with a direct antiferromagnetic exchange interaction between localized moments. Ferromagnetically long-range ordered state coexisting with the Kondo screening shows a continuous quantum phase transition to the Kondo singlet state. We obtain the value of the critical point where the magnetizations of the localized moments and the conduction electrons vanish. The magnetization curves yield a universal critical exponent independent of the filling factors and the strength of the interaction between localized moments. It is shown that the direct exchange interaction between localized moments introduces another phase transition from an antiferromagnetic ordering to a ferromagnetic ordering for small Kondo exchange interaction. We also explain the local minimum of the Kondo temperature in recent experiments.Comment: 6 pages, 5 figures, final versio
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