2003/05/13 by E. Abad, Jonathan L. Bentz, G. Nicolis +1
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1016/s0378-4371(03)00272-3
21 pages (including 12 figures and 4 tables), uses revtex4.cls, accepted for publication in Physica A
openalex publication_date 2003/05/13 · arxiv created 2003/05/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An analytical method based on the classical ruin problem is developed to compute the mean reaction time between two walkers undergoing a generalized random walk on a 1d lattice. At each time step, either both walkers diffuse simultaneously with probability p (synchronous event) or one of them diffuses while the other remains immobile with complementary probability (asynchronous event). Reaction takes place through same site occupation or position exchange. We study the influence of the degree of synchronicity p of the walkers and the lattice size N on the global reaction's efficiency. For odd N, the purely synchronous case (p=1) is always the most effective one, while for even N, the encounter time is minimized by a combination of synchronous and asynchronous events. This new parity effect is fully confirmed by Monte Carlo simulations on 1d lattices as well as for 2d and 3d lattices. In contrast, the 1d continuum approximation valid for sufficiently large lattices predicts a monotonic increase of the efficiency as a function of p. The relevance of the model for several research areas is briefly discussed.