不稳定轨道的渐近边界层方法：单个scar波函数的半经典
Asymptotic boundary layer method for unstable trajectories: Semiclassics for individual scar wavefunctions
摘要：
我们扩展的渐近边界层（ABL）的方法，最初开发的稳定的谐振器模式，局部不稳定的周期轨道周围的个别波函数的描述。该方法适用于描述完全或部分混沌量子系统中的疤痕态，也允许存在光滑和尖锐的势，以及磁场。我们认为，分界线波函数提供了一个单一的波函数的疤痕的最大贡献。这与早先关于波函数渐近性和疤痕态量子化条件的结果一致。的ABL形式主义的预测进行了比较与精确的数值解的带状谐振器与抛物线约束势和磁场。
英文摘要：
We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wavefunctions localized around unstable periodic orbits. The formalism applies to the description of scar states in fully or partially chaotic quantum systems, and also allows for the presence of smooth and sharp potentials, as well as magnetic fields. We argue that the separatrix wave function provides the largest contribution to the scars on a single wave function. This agrees with earlier results on the wave-function asymptotics and on the quantization condition of the scar states. Predictions of the ABL formalism are compared with the exact numerical solution for a strip resonator with a parabolic confinement potential and a magnetic field.
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