Persistence of instanton connections in chemical reactions with time dependent rates

TL;DR

This paper investigates how the phase space topology of chemical reaction systems, modeled via Hamiltonian dynamics, remains stable under small time-dependent rate variations, enabling qualitative insights from autonomous systems to be extended.

Contribution

It demonstrates the persistence of phase space structures in Hamiltonian models of chemical reactions under small time-dependent rate perturbations, with both concrete examples and general results.

Findings

Phase space topology is robust under small time-dependent perturbations.

Qualitative behavior of autonomous systems can be applied to time-dependent cases.

Robustness allows extension of instanton connection analysis to variable-rate reactions.

Abstract

The evolution of a system of chemical reactions can be studied, in the eikonal approximation, by means of a Hamiltonian dynamical system. The fixed points of this dynamical system represent the different states in which the chemical system can be found, and the connections among them represent instantons or optimal paths linking these states. We study the relation between the phase portrait of the Hamiltonian system representing a set of chemical reactions with constant rates and the corresponding system when these rates vary in time. We show that the topology of the phase space is robust for small time-dependent perturbations in concrete examples and state general results when possible. This robustness allows us to apply some of the conclusions on the qualitative behavior of the autonomous system to the time-dependent situation.