Hyperspherical Analysis of Dimer-Dimer Scattering in One-Dimensional Systems

TL;DR

This paper develops a hyperspherical method combined with a discretization technique to analyze four-body scattering in 1D quantum systems, successfully benchmarking against known solutions and exploring new non-integrable regimes.

Contribution

It introduces a novel computational framework using AHR and SVD for accurate four-body scattering analysis in 1D systems, including non-integrable regimes.

Findings

Excellent agreement with analytical results in integrable regimes

Identification of resonant scattering length enhancement

Observation of tetramer formation in non-integrable regimes

Abstract

We present a comprehensive analysis of four-body scattering in one-dimensional (1D) quantum systems using the adiabatic hyperspherical representation (AHR). Focusing on dimer-dimer collisions between two species of fermions interacting via the sinh-cosh potential, we implement the slow variable discretization (SVD) method to overcome numerical challenges posed by sharp avoided crossings in the potential curves. Our numerical approach is benchmarked against exact analytical results available in integrable regimes, demonstrating excellent agreement. We further explore non-integrable regimes where no analytical solutions exist, revealing novel features such as resonant enhancement of the scattering length associated with tetramer formation. These results highlight the power and flexibility of the AHR+SVD framework for accurate few-body scattering calculations in low-dimensional quantum systems, and establish a foundation for future investigations of universal few-body physics in ultracold gases.