Coupled Microwave Billiards as a Model for Symmetry Breaking

Abstract

Two superconducting microwave billiards have been electromagnetically coupled in a variable way. The spectrum of the entire system has been measured and the spectral statistics analyzed as a function of the coupling strength. It is shown that the results can be understood in terms of a random matrix model of quantum mechanical symmetry breaking -- as e.g. the violation of parity or isospin in nuclear physics.Comment: 4 pages, 5 figure

Analyzing symmetry breaking within a chaotic quantum system via Bayesian inference

“…The physical results of the present analysis show that the strongest coupling realized in the microwave experiment [1] has about the same size as the coupling found in [18] to occur between states of different isospin in 26 Al. The strongest coupling treated in the present paper causes about 25% mixing between the two classes of levels, i.e.…”

“…The technical realization of the coupling has been described in Ref. [1]. In the frequency range of 0 to 16 GHz, the complete spectra of the two stadia displayed 608 and 883 resonances in the (γ = 1) stadium and the (γ = 1.8) stadium, respectively.…”

“…Good examples of the experimental and theoretical efforts already invested into this problem, are the cases of isospin mixing [16][17][18], of parity violation in heavy nuclei [19], of the breaking of certain atomic and molecular symmetries [15,20]. The experiment performed in [1] provides a general model for these case studies.…”

Statistical behavior and symmetry tests

“…Experimentally the distribution is intermediate between the one-GOE and two-GOE distributions [7,8,10]. This agrees with predictions, fi rst by Dyson [18] and later by Pandey [19] There are no other direct tests in nuclei, but there are extensive results in " analog" systems: acoustic resonances in quartz blocks [21] and electromagnetic resonances in in superconducting microwave billiards [22]. In both of these experiments the magnitude of the symmetry-breaking was varied -in the former case by adjusting the length of the transmission line between the billiards and in the latter case by physically removing part of the block.…”

Level curvature distribution in a model of two uncoupled chaotic subsystems

“…In fact, an ideal experimental realisation of our model may be the system of two superconduction microwave billiards coupled by an antenna in a variable way [19]. Although, in real experiments of this type the coupling was changed in large discrete increments, it is in principle possible to change it in a much more controllable way, and to study level dynamics induced by such a coupling.…”