Fast algorithms for classical $X\to 0$ diffusion-reaction processes

TL;DR

This paper introduces a quantum-inspired numerical scheme for simulating classical diffusion-reaction processes, optimizing computational efficiency by focusing on reaction-prone configurations.

Contribution

It develops a novel second quantized formulation and a multiple time step algorithm for efficient simulation of $X\to 0$ reactions.

Findings

Efficient simulation of reaction-diffusion processes.

Systematic design of optimized, multiple time step algorithms.

Focus on configurations where reactions are most probable.

Abstract

The Doi formalism treats a reaction-diffusion process as a quantum many-body problem. We use this second quantized formulation as a starting point to derive a numerical scheme for simulating $X\to 0$ reaction-diffusion processes, following a well-established time discretization procedure. In the case of a reaction zone localized in the configuration space, this formulation provides also a systematic way of designing an optimized, multiple time step algorithm, spending most of the computation time to sample the configurations where the reaction is likely to occur.