Semiclassical description of regular-to-chaotic tunneling in cavities

设计具有定向激光发射的光学腔是实验和理论研究的一个活跃领域。典型的腔具有规则和混沌运动共存的混合相空间。在这样的系统中，规则到混沌隧穿决定了实验相关的品质因子和远场发射模式。虽然对规则到混沌隧穿量子映射有很好的理论理解，在这个项目中，我们希望基于规则区域的可积近似，导出腔中规则到混沌隧穿率的量子力学预测。特别是，我们希望定量描述由于共振的影响而导致的隧穿率的增强。一个中心目标将是使用复杂路径的半经典描述。从这一点上，我们期望获得一个直观的图片，既规则到混沌隧穿和共振-这将有助于设计具有强定向发射和大品质因数的腔形，并与实验结果进行比较。

Designing optical cavities which exhibit directional lasing emission is anactive area of experimental and theoretical research.Typical cavities have a mixed phase space in which regions of regular andchaotic motion coexist.In such systems, regular-to-chaotic tunneling determines the experimentallyrelevant quality factors and the far-field emission pattern.While an excellent theoretical understanding of regular-to-chaotic tunneling inquantum maps is available, this is not yet the case for cavities.In this project we want to derive quantum-mechanical predictionsfor regular-to-chaotic tunneling rates in cavitiesbased on integrable approximations of the regular region.In particular we want to quantitatively describethe enhancement of tunneling rates due to the influenceof resonance-assisted tunneling.A central goal will be the semiclassical description using complex paths.From this we expect to obtain an intuitive picture ofboth regular-to-chaotic tunneling and resonance-assisted tunneling in cavities.This will allow for designing cavity shapeswith strongly directional emission and large quality factorsand for comparing with experimental results.