论文标题
小型和中间体积的冬季（或三角洲）型号
Winter (or delta-shell) Model at Small and Intermediate Volumes
论文作者
论文摘要
我们考虑以有限体积的冬季（或三角壳）模型，描述了一个小的谐振腔，弱耦合到大型的腔体，用于小体积和中等体积（长度）。通过将n定义为大腔与小腔的长度的比率，我们研究了对称情况n = 1，其中两个空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，研究了从简单的量子振荡系统到具有共振光谱的系统的过渡。我们发现，每个共振状态都以有限的体积为代表，每个状态都在特定的耦合区域中共鸣，围绕在非常小的耦合处产生共鸣的状态。 在上述n个情况下，我们为粒子矩（大约）将其扰动序列恢复到腔之间的所有顺序中的颗粒动量。这些新的扩展与该顺序相当迅速地融合，令人惊讶地提供了耦合中均匀的近似值，并且在低能量下同样可以工作。 我们构建了一个具有清晰的物理图片的第一个重新启动方案，该方案基于功能序列的扩展以及基于递归方程的第二个方案。这两个方案在领先顺序上重合，虽然它们与近代领先的顺序不同。特别是，递归方案实现了第一个方案中生成的函数序列扩展的近似重新介绍。
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.
