费米子准一维多体问题的基准测试
Benchmarking the fermionic quasi-1D many-body problem
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中文总结 AI 辅助
该研究通过基准测试耦合道方法与三维问题导出的精确低能理论，发现仅重现两体散射振幅不足以构建准一维费米子的正确有效低能理论，需明确包含少体关联。
中文摘要 AI 辅助
我们通过将耦合道方法与从 underlying 三维问题导出的精确低能理论在弱吸引和强吸引极限下进行基准测试，研究准一维费米子系统的有效一维模型的有效性。我们表明，仅重现精确的两体散射振幅不足以构建准一维费米子的正确有效低能理论。在弱吸引区域，它无法捕获由横向激发诱导的涌现三体相互作用；在强吸引区域，它给出的原子-二聚体散射长度对三维散射长度的依赖关系不正确。这些结果证明了仅基于两体物理的有效一维描述的局限性，并强调需要在准一维系统中明确包含少体关联。
英文摘要
We investigate the validity of effective one-dimensional models for quasi-1D fermionic systems by benchmarking a coupled-channel approach against the exact low-energy theory derived from the underlying three-dimensional problem in the weakly and strongly attractive limits. We show that reproducing the exact two-body scattering amplitude is insufficient to construct the correct effective low-energy theory of quasi-1D fermions. In the weakly attractive regime, it does not capture the emergent three-body interaction induced by transverse excitations. In the strongly attractive regime, it yields an atom-dimer scattering length with an incorrect dependence on the three-dimensional scattering length. These results demonstrate the limitations of effective one-dimensional descriptions based solely on two-body physics and highlight the need to explicitly include few-body correlations in quasi-1D systems.
