Limits of Statistical Models of Ultracold Complex Lifetimes

TL;DR

This paper introduces a statistical model using random matrix theory and quantum defect theory to simulate ultracold collision complex lifetimes, addressing computational limitations of traditional methods.

Contribution

The work develops a new statistical approach that approximates full close-coupling calculations, providing insights into collision complex lifetimes across different resonance regimes.

Findings

Model agrees with RRKM prediction in dense resonance limit

Physics governed by threshold behavior in sparse resonance limit

Close-coupling calculations may be insufficient to explain long lifetimes

Abstract

The puzzle of "sticky collisions," in which molecular collision complexes exhibit unexpectedly long lifetimes, remains an unresolved mystery. A central challenge to solving this mystery is that traditional close-coupling calculations remain limited by the vast computational cost needed to take into account all the degrees of freedom involved in the collision. In this work, we propose a statistical model designed to simulate the result of full close-coupling calculations, with the goal of collecting statistics about reasonable lifetimes of collision complexes. To do so, we numerically sample resonances using random matrix theory and utilize results from quantum defect theory to calculate scattering properties and lifetimes. We find that in the limit of dense resonances, our theory agrees well with the Rice-Ramsperger-Kassel-Markus (RRKM) prediction, whereas in the limit of sparse resonances, the physics is governed by threshold behavior rather than resonant effects. By comparing these predictions to experimental results in two limits, we argue that close-coupling calculations alone may be insufficient to resolve the issue of long lifetimes.