Rare Events Statistics in Reaction--Diffusion Systems

TL;DR

This paper introduces an efficient semiclassical method to compute the probabilities of rare events in reaction--diffusion systems by analyzing the system's quantum Hamiltonian and its phase space dynamics.

Contribution

It presents a novel semiclassical approach to evaluate large deviation probabilities in reaction--diffusion systems, with applications demonstrated through illustrative examples.

Findings

Effective calculation of rare event probabilities

Application to multiple reaction--diffusion models

Insight into the phase space structure of these systems

Abstract

We develop an efficient method to calculate probabilities of large deviations from the typical behavior (rare events) in reaction--diffusion systems. The method is based on a semiclassical treatment of underlying "quantum" Hamiltonian, encoding the system's evolution. To this end we formulate corresponding canonical dynamical system and investigate its phase portrait. The method is presented for a number of pedagogical examples.