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- W2022656148 abstract "We study diffusion-limited pair annihilation $A+stackrel{ensuremath{rightarrow}}{A}0$ on one-dimensional lattices with inhomogeneous nearest-neighbor hopping in the limit of an infinite reaction rate. We obtain a simple exact expression for the particle concentration ${ensuremath{rho}}_{k}(t)$ of the many-particle system in terms of the conditional probabilities $P(m;t|l;0)$ for a single random walker in a dual medium. For some disordered systems with an initially randomly filled lattice this leads asymptotically to $overline{ensuremath{rho}(t)}=overline{P(0;2t|0;0)}$ for the disorder-averaged particle density. We also obtain interesting exact relations for single-particle conditional probabilities in random media related by duality, such as random-barrier and random-trap systems. For some specific random-barrier systems the Smoluchovsky approach to diffusion-limited annihilation turns out to fail." @default.
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- W2022656148 title "Annihilating random walks in one-dimensional disordered media" @default.
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- W2022656148 doi "https://doi.org/10.1103/physreve.57.2563" @default.
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