Dynamics and decay rates of a time-dependent two-saddle system

TL;DR

This paper develops a new method to analyze decay rates in complex physical systems with multiple time-dependent saddle points, overcoming previous challenges related to fractal phase space structures.

Contribution

It introduces an approximately recrossing-free dividing surface for a two-saddle system, enabling accurate computation of time-resolved decay rates.

Findings

Successful construction of a dividing surface reducing recrossings

Multiple methods for calculating instantaneous decay rates demonstrated

Enhanced understanding of decay dynamics in multi-saddle systems

Abstract

The framework of transition state theory (TST) provides a powerful way for analyzing the dynamics of physical and chemical reactions. While TST has already been successfully used to obtain reaction rates for systems with a single time-dependent saddle point, multiple driven saddles have proven challenging because of their fractal-like phase space structure. This paper presents the construction of an approximately recrossing-free dividing surface based on the normally hyperbolic invariant manifold in a time-dependent two-saddle model system. Based on this, multiple methods for obtaining instantaneous (time-resolved) decay rates of the underlying activated complex are presented and their results discussed.