任意表示中的各向同性接触力：非均匀少体问题和低维
Isotropic contact forces in arbitrary representation: heterogeneous few-body problems and low dimensions
摘要：
Bethe-Peierls渐近的方法，模型成对的短程力的接触条件被引入到任意表示的空间尺寸小于或等于3。形式主义适用于各种情况，重点放在动量表示。在存在横向谐波约束的情况下，在这种形式主义中导出了朝向二维（2D）或一维（1D）物理的降维。将相互作用系统的平均能量与单粒子密度矩阵的渐近行为联系起来的能量定理说明了第二量子化形式的方法。导出了包含Bethe-Peierls接触条件的少体系统的积分方程。在三维空间中，对于支持Efimov态的三体系统，为了从SkorniakovTer-Martirosian方程得到普遍的结果，引入了节点条件，避免了Thomas坍缩.导出了四体束缚态本征方程，计算了二维“3+1”玻色基态随质量比的变化。
英文摘要：
The Bethe-Peierls asymptotic approach which models pairwise short-range forces by contact conditions is introduced in arbitrary representation for spatial dimensions less than or equal to 3. The formalism is applied in various situations and emphasis is put on the momentum representation. In the presence of a transverse harmonic confinement, dimensional reduction toward two-dimensional (2D) or one-dimensional (1D) physics is derived within this formalism. The energy theorem relating the mean energy of an interacting system to the asymptotic behavior of the one-particle density matrix illustrates the method in its second quantized form. Integral equations that encapsulate the Bethe-Peierls contact condition for few-body systems are derived. In three dimensions, for three-body systems supporting Efimov states, a nodal condition is introduced in order to obtain universal results from the Skorniakov Ter-Martirosian equation and the Thomas collapse is avoided. Four-body bound state eigenequations are derived and the 2D '3+1' bosonic ground state is computed as a function of the mass ratio.
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