Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards

doi:10.1088/1674-1056/ab3f96

Abstract We report on the experimental investigation of the properties of the eigenvalues and wavefunctions and the fluctuation properties of the scattering matrix of closed and open billiards, respectively, of which the classical dynamics undergoes a transition from integrable via almost integrable to fully chaotic. To realize such a system, we chose a billiard with a 60° sector shape of which the classical dynamics is integrable, and introduced circular scatterers of varying number, size, and position. The spectral properties of generic quantum systems of which the classical counterpart is either integrable or chaotic are universal and well understood. If, however, the classical dynamics is pseudo-integrable or almost-integrable, they exhibit a non-universal intermediate statistics, for which analytical results are known only in a few cases, e.g., if it corresponds to semi-Poisson statistics. Since the latter is, above all, clearly distinguishable from those of integrable and chaotic systems, our aim was to design a billiard with these features which indeed is achievable by adding just one scatterer of appropriate size and position to the sector billiard. We demonstrated that, while the spectral properties of almost-integrable billiards are sensitive to the classical dynamics, this is not the case for the distribution of the wavefunction components, which was analyzed in terms of the strength distribution, and the fluctuation properties of the scattering matrix which coincide with those of typical, fully chaotic systems.

Keywords: wave chaos quantum billiards microwave billiards random matrix theory

Received: 13 July 2019
Revised: 10 August 2019
Accepted manuscript online:

PACS:	03.65.Ge	(Solutions of wave equations: bound states)
	03.65.Sq	(Semiclassical theories and applications)
	05.45.Mt	(Quantum chaos; semiclassical methods)
	24.60.Ky	(Fluctuation phenomena)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11775100, 11775101, and 11961131009).

Corresponding Authors: Barbara Dietz
E-mail: dietz@lzu.edu.cn

Cite this article:

Runzu Zhang(张润祖), Weihua Zhang(张为华), Barbara Dietz, Guozhi Chai(柴国志), Liang Huang(黄亮) Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards 2019 Chin. Phys. B 28 100502

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Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards

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