发表机构
Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新研究院武汉物理与数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出通用框架，解析相交δ势垒的量子散射，揭示通道变化由相移承载，并精确求解量子Galperin台球。
AI 中文摘要
我们为平面波在一类Gaudin万花筒模型中的散射发展了一个通用框架，该类模型由在公共点相交的直线δ势垒组成。投影的Lippmann-Schwinger方程分解为奇异部分、由几何移动规则生成的有限极点闭合以及正则余项，出射态为圆上的原子测度。在特殊角度π/N处，相交势垒生成二面体群D_N，通道数保持不变，而在一般角度下，通道被创建和湮灭，当穿越临界方向时从零权重平滑打开。这在概率中不留下奇异痕迹，而是由相移承载，这是一种超越坐标Bethe ansatz的量子-经典对应。相同的方程精确求解量子Galperin台球，镜像方法将其简化为单一线性系统，其相移以闭式形式给出。
英文摘要
We develop a general framework for the scattering of a plane wave by a class of Gaudin kaleidoscope models: straight $δ$-potential barriers intersecting at a common point. The projected Lippmann-Schwinger equations split into a singular part, a finite pole closure generated by a geometric moving rule, and a regular remainder, the outgoing state being an atomic measure on the circle. At the special angles $π/N$, where the intersecting barriers generate the dihedral group $D_N$, the number of channels stays fixed, whereas at generic angles channels are created and destroyed, opening smoothly from zero weight as a critical direction is crossed. This leaves no singular trace in the probabilities, being carried instead by the phase shifts, a quantum-classical correspondence beyond the reach of the coordinate Bethe ansatz. The same equations solve the quantum Galperin billiards exactly, the method of images reducing them to a single linear system whose phase shifts follow in closed form.
