Quantized invariant tori in Andreev billiards of mixed phase space

TL;DR

This paper demonstrates that the spectrum of Andreev billiards with mixed phase space can be decomposed into regular and irregular parts, confirming the validity of an EBK-like quantization scheme through numerical analysis.

Contribution

It provides the first numerical validation of an EBK-like quantization scheme for individual eigenstates in Andreev billiards with mixed phase space.

Findings

Spectrum decomposes into regular and irregular parts

Validation of EBK-like quantization scheme for individual eigenstates

Numerical confirmation of quantization accuracy

Abstract

Comparing the results of exact quantum calculations and those obtained from the EBK-like quantization scheme of Silvestrov et al [Phys. Rev. Lett. 90, 116801 (2003)] we show that the spectrum of Andreev billiards of mixed phase space can basically be decomposed into a regular and an irregular part, similarly to normal billiards. We provide the first numerical confirmation of the validity of this quantization scheme for individual eigenstates and discuss its accuracy.