Abstract
The probabilistic dynamics of a pair of particles which can mutually annihilate in the course of their random walk on a lattice is considered and analytically found for d=1 and d=2. In view of available recent experiments achieved on the femtosecond scale, emphasis is put on the necessity of a full continuous-time, discrete-space solution at all times. Quantities of physical interest are calculated at any time, including the total pair survival probability N(t) and the two-particle correlation function. As a by-product, the lattice version allows for a precise regularization of the continuous-space framework, which is ill-conditionned for d≥2; this being done, formal generalization to any real dimensionality can be straightforwardly performed.
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Aslangul, C. Mutual Annihilation of Two Diffusing Particles in One- and Two-Dimensional Lattices. Journal of Statistical Physics 94, 219–240 (1999). https://doi.org/10.1023/A:1004567430632
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DOI: https://doi.org/10.1023/A:1004567430632