Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards

doi:10.1088/1674-1056/ab3f96

中国物理B ›› 2019, Vol. 28 ›› Issue (10): 100502-100502.doi: 10.1088/1674-1056/ab3f96

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards

Runzu Zhang(张润祖), Weihua Zhang(张为华), Barbara Dietz, Guozhi Chai(柴国志), Liang Huang(黄亮)

1 School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China;
2 Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou 730000, China

收稿日期:2019-07-13 修回日期:2019-08-10 出版日期:2019-10-05 发布日期:2019-10-05
通讯作者: Barbara Dietz E-mail:dietz@lzu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11775100, 11775101, and 11961131009).

Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards

Runzu Zhang(张润祖)^1,2, Weihua Zhang(张为华)^1,2, Barbara Dietz^1,2, Guozhi Chai(柴国志)², Liang Huang(黄亮)^1,2

1 School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China;
2 Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou 730000, China

Received:2019-07-13 Revised:2019-08-10 Online:2019-10-05 Published:2019-10-05
Contact: Barbara Dietz E-mail:dietz@lzu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11775100, 11775101, and 11961131009).

摘要/Abstract

摘要： 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.

关键词: wave chaos, quantum billiards, microwave billiards, random matrix theory

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.

Key words: wave chaos, quantum billiards, microwave billiards, random matrix theory

中图分类号: (Solutions of wave equations: bound states)

03.65.Ge

03.65.Sq (Semiclassical theories and applications) 05.45.Mt (Quantum chaos; semiclassical methods) 24.60.Ky (Fluctuation phenomena)

张润祖, 张为华, Barbara Dietz, 柴国志, 黄亮. Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards[J]. 中国物理B, 2019, 28(10): 100502-100502.

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[J]. Chin. Phys. B, 2019, 28(10): 100502-100502.

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Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards

Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards

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