Abstract
In ballistic open quantum systems, one often observes that the resonances in the complex-energy plane form a clear chain structure. Taking the open three-disk system as a paradigmatic model system, we investigate how this chain structure is reflected in the resonance states and how it is connected to the underlying classical dynamics. Using an efficient scattering approach, we observe that resonance states along one chain are clearly correlated, while resonance states of different chains show an anticorrelation. Studying the phase-space representations of the resonance states, we find that their localization in phase space oscillates between different regions of the classical trapped set as one moves along the chains, and that these oscillations are connected to a modulation of the resonance spacing. A single resonance chain is thus not a WKB quantization of a single periodic orbit, but the structure of several oscillating chains arises from the interaction of several periodic orbits. We illuminate the physical mechanism behind these findings by combining the semiclassical cycle expansion with a quantum graph model.
Highlights
The study of geometrically open quantum systems is a subject of intense research, with recent interest driven in equal parts by concrete applications and deep fundamental questions [5,6,7]
Taking the open three-disk system as a paradigmatic model system, we investigate how this chain structure is reflected in the resonance states and how it is connected to the underlying classical dynamics
Deeper in the semiclassical limit, we find that the merging of resonance chains coincides with an increased population of the classical trapped set by long-lived resonance states
Summary
The study of geometrically open (leaky) quantum systems is a subject of intense research, with recent interest driven in equal parts by concrete applications (including electronic transport [1, 2] and microcavity lasers [3, 4]) and deep fundamental questions [5,6,7]. In order to extract the underlying mechanism behind these correlations and modulations, we formulate an approximate correspondence of the three-disk system with an open quantum graph, consisting of two edges of different lengths This correspondence holds in the leading order of the cycle expansion, and implies that the systematic correlations and interactions of the chains originate from the approximate commensurability of the fundamental periodic orbits in the system. We explain how this method can be used to efficiently calculate Poincaré–Husimi distributions, as well as the symmetric phase-space distributions proposed by Ermann et al [49]
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