Experimental investigation of the elastic enhancement factor in a transient region between regular and chaotic dynamics

TL;DR

This study experimentally examines the elastic enhancement factor in microwave cavities simulating quantum billiards, revealing deviations from theoretical predictions in systems between regular and chaotic dynamics.

Contribution

It provides the first experimental comparison of the elastic enhancement factor in a transient regime between regular and chaotic quantum billiards.

Findings

The elastic enhancement factor in the rectangular cavity is below the integrable system value of 3.

The enhancement factor is higher than in a chaotic rough cavity.

Results align with a recent two-channel coupling model and differ from Random Matrix Theory predictions.

Abstract

We present the results of an experimental study of the elastic enhancement factor W for a microwave rectangular cavity simulating a two-dimensional quantum billiard in a transient region between regular and chaotic dynamics. The cavity was coupled to a vector network analyzer via two microwave antennas. The departure of the system from the integrable one due to presence of antennas acting as scatterers is characterised by the parameter of chaoticity k = 2.8. The experimental results for the rectangular cavity are compared with the ones obtained for a microwave rough cavity simulating a chaotic quantum billiard. The experimental results were obtained for the frequency range v = 16 - 18.5 GHz and moderate absorption strength y = 5.2 - 7.4. We show that the elastic enhancement factor for the rectangular cavity lies below the theoretical value W = 3 predicted for integrable systems and it is significantly higher than the one obtained for the rough cavity. The results obtained for the microwave rough cavity are smaller than the ones obtained within the framework of Random Matrix Theory and lie between them and the ones predicted within a recently introduced model of the two-channel coupling (V. Sokolov and O. Zhirov, arXiv:1411.6211v2[nucl-th], 12 Dec 2014).