Superscars in billiards -- A model for doorway states in quantum spectra

TL;DR

This paper investigates superscars in billiards as a model for doorway states in quantum spectra, using new statistical measures and theoretical models to understand their spectral properties.

Contribution

It introduces novel statistical observables and applies Random Matrix Theory and random plane waves to analyze superscars in billiards, advancing understanding of doorway mechanisms.

Findings

Distribution of maximum coupling coefficient matches theoretical predictions.

Directed spatial correlators reveal spatial structure of superscars.

Consistent explanation of experimental data using RMT and random plane waves.

Abstract

In a unifying way, the doorway mechanism explains spectral properties in a rich variety of open mesoscopic quantum systems, ranging from atoms to nuclei. A distinct state and a background of other states couple to each other which sensitively affects the strength function. The recently measured superscars in the barrier billiard provide an ideal model for an in--depth investigation of this mechanism. We introduce two new statistical observables, the full distribution of the maximum coupling coefficient to the doorway and directed spatial correlators. Using Random Matrix Theory and random plane waves, we obtain a consistent understanding of the experimental data.