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

Area of Science:

• Physical Chemistry
• Statistical Mechanics
• Surface Science

Background:

• Particle diffusion in confined environments is modeled as surface hops.
• The surface hopping propagator is crucial for understanding diffusion-influenced reactions.

Purpose of the Study:

• To derive explicit formulas for the surface hopping propagator.
• To analyze its role in diffusion-influenced reactions and surface phenomena.
• To investigate particle behavior in various confinement geometries.

Main Methods:

• Derivation of explicit formulas for the surface hopping propagator.
• Analysis of related quantities like first-passage time distribution and reaction rate.
• Investigation across Euclidean domains: half-space, circular annuli, cylinders, and spherical shells.

Main Results:

• Explicit formulas for the surface hopping propagator were derived for multiple geometries.
• The propagator's behavior was analyzed for both 'immortal' and 'mortal' particles.
• Theoretical groundwork was established for studying diffusion-mediated surface phenomena.

Conclusions:

• The surface hopping propagator is central to understanding diffusion-influenced reactions.
• The derived formulas offer a theoretical basis for analyzing diffusion on surfaces.
• This work facilitates the study of complex surface phenomena in confined systems.