论文标题
量子系统的符合性不变性和倒数问题的逆问题
Symplectic invariants of semitoric systems and the inverse problem for quantum systems
论文作者
论文摘要
大约十年前，简单的半牙本系统是根据一系列不变式的分类，基本上由凸多边形给出，一些标记点对应于焦点对象奇异性。每个标记的点都赋予系统的符号不变性标签。我们将回顾这些不变的构建，并解释如何在不同情况下概括或应用它们。这些应用之一涉及量子整合系统和相应的反问题，该系统询问在频谱中可以找到多少相关的经典系统信息。解决此问题的一种方法是尝试在频谱中计算不变性。我们将解释如何对于某些半生系统的某些不变，并在这个方向上讨论一个空旷的问题。
Simple semitoric systems were classified about ten years ago in terms of a collection of invariants, essentially given by a convex polygon with some marked points corresponding to focus-focus singularities. Each marked point is endowed with labels which are symplectic invariants of the system. We will review the construction of these invariants, and explain how they have been generalized or applied in different contexts. One of these applications concerns quantum integrable systems and the corresponding inverse problem, which asks how much information of the associated classical system can be found in the spectrum. An approach to this problem has been to try to compute invariants in the spectrum. We will explain how this has been recently achieved for some of the invariants of semitoric systems, and discuss an open question in this direction.
