Toward extracting scattering phase shift from integrated correlation functions III: coupled-channels

TL;DR

This paper extends a formalism linking integrated correlation functions to scattering phase shifts to coupled-channel systems, validated through models and simulations, with rapid convergence suggesting practical advantages.

Contribution

It introduces a new relation for coupled-channel systems that connects correlation functions to phase shifts without involving inelasticity, extending previous single-channel work.

Findings

Derived a coupled-channel relation similar to the single-channel case.

Validated the relation with exactly solvable models and Monte Carlo simulations.

Observed rapid convergence to the infinite volume limit with increasing trap size.

Abstract

The formalism developed in Refs.\cite{Guo:2023ecc,Guo:2024zal} that connects integrated correlation function of a trapped two-particle system to infinite volume scattering phase shift is further extended to coupled-channel systems in the present work. Using a trapped non-relativistic two-channel system as an example, a new relation is derived that retains the same structure as in the single channel, and has explicit dependence on the phase shifts in both channels but not on the inelasticity. The relation is illustrated by an exactly solvable coupled-channel quantum mechanical model with contact interactions. It is further validated by path integral Monte Carlo simulation of a quasi-one-dimensional model that can admit general interaction potentials. In all cases, we found rapid convergence to the infinite volume limit as the trap size is increased, even at short times, making it potentially a good candidate to overcome signal-to-noise issues in Monte Carlo applications.