Weyl asymptotics: From closed to open systems

TL;DR

This study experimentally investigates the transition from closed to open quantum systems using microwave billiards, analyzing resonance behavior and providing evidence for the fractal Weyl conjecture.

Contribution

It demonstrates the smooth change in Weyl asymptotics during the transition from closed to open systems and discusses resonance extraction challenges.

Findings

Weyl asymptotic exponent decreases from 2 to a non-integer value as system opens

Resonance extraction becomes more difficult in open systems

Experimental support for the fractal Weyl conjecture for resonances

Abstract

We present microwave experiments on the symmetry reduced 5-disk billiard studying the transition from a closed to an open system. The measured microwave reflection signal is analyzed by means of the harmonic inversion and the counting function of the resulting resonances is studied. For the closed system this counting function shows the Weyl asymptotic with a leading exponent equal to 2. By opening the system successively this exponent decreases smoothly to an non-integer value. For the open systems the extraction of resonances by the harmonic inversion becomes more challenging and the arising difficulties are discussed. The results can be interpreted as a first experimental indication for the fractal Weyl conjecture for resonances.