A Model for Scattering with Proliferating Resonances: Many Coupled Square Wells

TL;DR

This paper introduces a multichannel square-well model to describe elastic scattering with many resonances, useful for ultracold molecule experiments, and analyzes the transition from integrable to chaotic behavior.

Contribution

It provides a semi-analytic multichannel model with a statistical ensemble for parameters, capturing resonance behavior and the crossover from integrable to chaotic scattering.

Findings

Model captures many coupled resonances near threshold

Probability distributions fit Brody distribution well

Demonstrates crossover from integrable to chaotic scattering

Abstract

We present a multichannel model for elastic interactions, comprised of an arbitrary number of coupled finite square-well potentials, and derive semi-analytic solutions for its scattering behavior. Despite the model's simplicity, it is flexible enough to include many coupled short-ranged resonances in the vicinity of the collision threshold, as is necessary to describe ongoing experiments in ultracold molecules and lanthanide atoms. We also introduce a simple, but physically realistic, statistical ensemble for parameters in this model. We compute the resulting probability distributions of nearest-neighbor resonance spacings and analyze them by fitting to the Brody distribution. We quantify the ability of alternative distribution functions, for resonance spacing and resonance number variance, to describe the crossover regime. The analysis demonstrates that the multichannel square-well model with the chosen ensemble of parameters naturally captures the crossover from integrable to chaotic scattering as a function of closed channel coupling strength.