Formation and interaction of resonance chains in the open three-disk system

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.

Keywords

• resonances
• wave scattering
• chaotic systems
• 05.45.Mt
• 03.65.Nk
• 42.25.Bs