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

• URL: http://arxiv.org/abs/2506.01233v1
• Date: Mon, 02 Jun 2025 01:11:30 GMT
• Title: Hyperspherical Analysis of Dimer-Dimer Scattering in One-Dimensional Systems
• Abstract summary: We present a comprehensive analysis of four-body scattering in 1D quantum systems using the adiabatic hyperspherical representation (AHR)<n>We implement the slow variable discretization (SVD) method to overcome numerical challenges posed by sharp avoided crossings in the potential curves.<n>Results highlight the power and flexibility of the AHR+SVD framework for accurate few-body scattering calculations in low-dimensional quantum systems.
• Score: 3.944954775892428
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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