Surface hopping propagator: An alternative approach to diffusion-influenced reactions

Denis S Grebenkov (1)

1 LPMC - Laboratoire de physique de la matière condensée

Dynamics of a particle diffusing in a confinement can be seen a sequence of bulk-diffusion-mediated hops on the confinement surface. Here, we investigate the surface hopping propagator that describes the position of the diffusing particle after a prescribed number of encounters with that surface. This quantity plays the central role in diffusion-influenced reactions and determines their most common characteristics such as the propagator, the first-passage time distribution, and the reaction rate. We derive explicit formulas for the surface hopping propagator and related quantities for several Euclidean domains: half-space, circular annuli, circular cylinders, and spherical shells. These results provide the theoretical ground for studying diffusion-mediated surface phenomena. The behavior of the surface hopping propagator is investigated for both "immortal" and "mortal" particles.

Mots clés: diffusion; escape problem; first passage time; mixed boundary condition

Domaines: Physique mathématique [math-ph]; Mécanique statistique [cond-mat.stat-mech]; Biophysique [physics.bio-ph]; Chimie-Physique [physics.chem-ph]; Physique Numérique [physics.comp-ph]; Analyse de données, Statistiques et Probabilités [physics.data-an]

Denis S Grebenkov. Surface hopping propagator: An alternative approach to diffusion-influenced reactions. Physical Review E , 2020, 102 (3), pp.032125. ⟨10.1103/PhysRevE.102.032125⟩. ⟨hal-03375467⟩