Institut de Physique Théorique, , CEA Saclay, 91191 Gif-sur-Yvette Cedex, France.
Philos Trans A Math Phys Eng Sci. 2013 Dec 16;372(2007):20120509. doi: 10.1098/rsta.2012.0509. Print 2014 Jan 28.
This survey article deals with a delta potential--also known as a point scatterer--on flat two- and three-dimensional tori. We introduce the main conjectures regarding the spectral and wave function statistics of this model in the so-called weak and strong coupling regimes. We report on recent progress as well as a number of open problems in this field.
本文讨论了平面二维和三维环面上的一个δ势——也称为点散射体。我们介绍了该模型在所谓的弱耦合和强耦合区域内的谱和波函数统计的主要猜想。我们报告了该领域的最新进展和一些开放性问题。