中小尺度冬季（或三角壳）模式
Winter (or delta-shell) Model at Small and Intermediate Volumes
摘要：
我们考虑有限体积的Winter（或三角壳）模型，描述了一个小的谐振腔弱耦合到一个大的，小的和中等体积（长度）。通过定义大腔长与小腔长之比N，我们研究了N=1的对称情况，即两个腔实际上具有相同的长度，以及N= 2，3，4的情况。通过在上述范围内增加N，研究了从简单量子振荡系统到具有共振谱的系统的跃迁。我们发现，每个谐振状态表示，在有限的体积，由一组状态，每一个谐振在一个特定的耦合区域，围绕一个状态谐振在非常小的耦合。我们导出了上述N种情况下粒子动量的高能展开式，它（近似）将它们的微扰级数归结为腔间耦合的所有阶数。这些新的扩展收敛相当快的顺序，提供，令人惊讶的是，一个统一的近似耦合，也工作，再次令人惊讶的是，在低能量。我们构造了第一个重建方案具有清晰的物理图像，这是基于函数级数展开，以及第二个计划的基础上的递归方程。这两种格式在首阶上一致，而在次首阶上不同，特别是递归格式实现了第一种格式中函数级数展开式的近似再确认。
英文摘要：
We consider Winter (or delta-shell) model at finite volume, describing a small resonating cavity weakly coupled to a large one, for small and intermediate volumes (lengths). By defining N as the ratio of the length of the large cavity over the small one, we study the symmetric case N=1, in which the two cavities actually have the same length, as well as the cases N=2,3,4. By increasing N in the above range, the transition from a simple quantum oscillating system to a system having a resonance spectrum is investigated. We find that each resonant state is represented, at finite volume, by a cluster of states, each one resonating in a specific coupling region, centered around a state resonating at very small couplings. We derive high-energy expansions for the particle momenta in the above N cases, which (approximately) resum their perturbative series to all orders in the coupling among the cavities. These new expansions converge rather quickly with the order, provide, surprisingly, a uniform approximation in the coupling and also work, again surprisingly, at low energies. We construct a first resummation scheme having a clear physical picture, which is based on a function-series expansion, as well as a second scheme based on a recursion equation. The two schemes coincide at leading order, while they differ from next-to-leading order on. In particular, the recursive scheme realizes an approximate resummation of the function-series expansion generated within the first scheme.
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