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.

Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

“…These theoretical findings have been confirmed experimentally in GaAs/AlGaAs (Harayama et al, 2003), GaAs and polymer microstadia . The observation of localization along multiple periodic orbits is consistent with a recent study of an open three-disk system (Weich et al, 2014) which relates this phenomenon to the formation and interaction of resonance chains in the complex frequency plane.…”

Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions

“…By this approach, in [6] resonance distributions were compared to the existent conjectures. Those investigations also revealed the striking formation of resonance chains, which triggered further numerical [2,35] and mathematical [34] studies.…”

Resonance Chains and Geometric Limits on Schottky Surfaces

“…The existence of these open conjectures motivated Borthwick to study the resonance spectrum on infinite volume hyperbolic surfaces numerically [4] and to a great surprise he observed that the resonances on 3-funneled Schottky surfaces are often highly ordered and form resonance chains. It has recently been shown in a numerical study by Barkhofen, Faure and the author [1] that these resonance chains can be understood by a generalized zeta function and are related to a clustering of the length spectrum on X and that the same kind of resonance chains also appear in various other physical systems (for details on the significance of resonance chains in physics we refer to [30] and references therein).…”