Demonstration of turnstiles as a chaotic ionization mechanism in Rydberg atoms

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.

Open quantum maps from complex scaling of kicked scattering systems

We derive open quantum maps from periodically kicked scattering systems and discuss the computation of their resonance spectra in terms of theoretically grounded methods, such as complex scaling and sufficiently weak absorbing potentials. In contrast, we also show that current implementations of open quantum maps, based on strong absorptive or even projective openings, fail to produce the resonance spectra of kicked scattering systems. This comparison pinpoints flaws in current implementations of open quantum maps, namely, the inability to separate resonance eigenvalues from the continuum as well as the presence of diffraction effects due to strong absorption. The reported deviations from the true resonance spectra appear, even if the openings do not affect the classical trapped set, and become appreciable for shorter-lived resonances, e.g., those associated with chaotic orbits. This makes the open quantum maps, which we derive in this paper, a valuable alternative for future explorations of quantum-chaotic scattering systems, for example, in the context of the fractal Weyl law. The results are illustrated for a quantum map model whose classical dynamics exhibits key features of ionization and a trapped set which is organized by a topological horseshoe.

Invariant manifolds and the geometry of front propagation in fluid flows

Recent theoretical and experimental work has demonstrated the existence of one-sided, invariant barriers to the propagation of reaction-diffusion fronts in quasi-two-dimensional periodically driven fluid flows. These barriers were called burning invariant manifolds (BIMs). We provide a detailed theoretical analysis of BIMs, providing criteria for their existence, a classification of their stability, a formalization of their barrier property, and mechanisms by which the barriers can be circumvented. This analysis assumes the sharp front limit and negligible feedback of the front on the fluid velocity. A low-dimensional dynamical systems analysis provides the core of our results.