A stochastic model and Monte Carlo algorithm for fluctuation-induced H$_2$ formation on the surface of interstellar dust grains

TL;DR

This paper introduces a stochastic model and Monte Carlo algorithm to simulate fluctuation-induced hydrogen molecule formation on interstellar dust grains, accounting for spatial inhomogeneities and segregation effects.

Contribution

It generalizes a stochastic simulation technique to model H$_2$ formation, incorporating spatially inhomogeneous, nonlinear integro-differential equations with random sources.

Findings

Segregation effects depend on source distribution and generation rate.

The stochastic particle method effectively captures spatial distribution and correlations.

The model reveals isotropic and stationary concentration fields in the system.

Abstract

A stochastic algorithm for simulation of fluctuation-induced kinetics of H$_2$ formation on grain surfaces is suggested as a generalization of the technique developed in our recent studies where this method was developed to describe the annihilation of spatially separate electrons and holes in a disordered semiconductor. The stochastic model is based on the spatially inhomogeneous, nonlinear integro-differential Smoluchowski equations with random source term. In this paper we derive the general system of Smoluchowski type equations for the formation of H$_2$ from two hydrogen atoms on the surface of interstellar dust grains with physisorption and chemisorption sites. We focus in this study on the spatial distribution, and numerically investigate the segregation in the case of a source with a continuous generation in time and randomly distributed in space. The stochastic particle method presented is based on a probabilistic interpretation of the underlying process as a stochastic Markov process of interacting particle system in discrete but randomly progressed time instances. The segregation is analyzed through the correlation analysis of the vector random field of concentrations which appears to be isotropic in space and stationary in time.