Open quantum maps from complex scaling of kicked scattering systems

Layered localization in a chaotic optical cavity

We propose and demonstrate the localization of resonant modes in a Limaçon optical microcavity with layered phase space involving both major and minor partial barriers. By regulating the openness of the cavity through the refractive index control, the minor partial barriers, which do not directly confine the long-lived resonant modes, are submerged successively into the leaky region. During the invalidation process of the minor partial barriers, it is found that the quality factor and the conjugate momentum of the resonant modes exhibit changes with the emergence of turning points. Such phenomena are attributed to the joint confinement effect by the minor partial barriers together with the major one in the layered phase space. This paper helps to improve the understanding of complex dynamics, and sheds light on the fine design of photonic devices with high performance.

Uniform Hyperbolicity of a Scattering Map with Lorentzian Potential

We show that a two-dimensional area-preserving map with Lorentzian potential is a topological horseshoe and uniformly hyperbolic in a certain parameter region. In particular, we closely examine the so-called sector condition, which is known to be a sufficient condition leading to the uniformly hyperbolicity of the system. The map will be suitable for testing the fractal Weyl law as it is ideally chaotic yet free from any discontinuities which necessarily invokes a serious effect in quantum mechanics such as diffraction or nonclassical effects. In addition, the map satisfies a reasonable physical boundary condition at infinity, thus it can be a good model describing the ionization process of atoms and molecules.