Experimental test of an extension of the Rosenzweig-Porter model to mixed integrable-chaotic systems experiencing time-reversal invariance violation

doi:10.1088/1674-1056/ad8a4e

中国物理B ›› 2024, Vol. 33 ›› Issue (12): 120501-120501.doi: 10.1088/1674-1056/ad8a4e

Experimental test of an extension of the Rosenzweig-Porter model to mixed integrable-chaotic systems experiencing time-reversal invariance violation

Xiaodong Zhang(张晓东)^1,2, Jiongning Che(车炯宁)^3,1, and Barbara Dietz^2,4,1,†

1 Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, and Key Laboratory of Quantum Theory and Applications of the Ministry of Education, Lanzhou University, Lanzhou 730000, China;
2 Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea;
3 Yangtze Delta Region Institute, University of Electronic Science and Technology of China, Huzhou 313001, China;
4 Basic Science Program, Korea University of Science and Technology (UST), Daejeon 34113, Korea

收稿日期:2024-09-14 修回日期:2024-10-14 接受日期:2024-10-23 出版日期:2024-12-15 发布日期:2024-12-04
通讯作者: Barbara Dietz E-mail:bdietzp@gmail.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11775100, 12247101, and 11961131009), Xiaodong Zhang acknowledges the financial support from the China Scholarship Council (Grant No. CSC-202306180087), and Barbara Dietz and Xiaodong Zhang acknowledge the financial support from the Institute for Basic Science in Korea (Grant No. IBS-R024-D1).

Experimental test of an extension of the Rosenzweig-Porter model to mixed integrable-chaotic systems experiencing time-reversal invariance violation

Xiaodong Zhang(张晓东)^1,2, Jiongning Che(车炯宁)^3,1, and Barbara Dietz^2,4,1,†

1 Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, and Key Laboratory of Quantum Theory and Applications of the Ministry of Education, Lanzhou University, Lanzhou 730000, China;
2 Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea;
3 Yangtze Delta Region Institute, University of Electronic Science and Technology of China, Huzhou 313001, China;
4 Basic Science Program, Korea University of Science and Technology (UST), Daejeon 34113, Korea

Received:2024-09-14 Revised:2024-10-14 Accepted:2024-10-23 Online:2024-12-15 Published:2024-12-04
Contact: Barbara Dietz E-mail:bdietzp@gmail.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11775100, 12247101, and 11961131009), Xiaodong Zhang acknowledges the financial support from the China Scholarship Council (Grant No. CSC-202306180087), and Barbara Dietz and Xiaodong Zhang acknowledge the financial support from the Institute for Basic Science in Korea (Grant No. IBS-R024-D1).

摘要/Abstract

摘要： We report on the theoretical and experimental investigations of the transition of a typical quantum system with mixed regular-integrable classical dynamics to one with violated time-reversal (${\mathcal T}$) invariance. The measurements are performed with a flat superconducting microwave resonator with circular shape in which chaoticity is induced by using either long antennas or inserting two circular disks into the cavity, and by magnetizing a ferrite disk placed at its center, which leads to violation of ${\mathcal T}$ invariance. We propose an extension of the Rosenzweig-Porter (RP) model, which interpolates between mixed regular-chaotic instead of integrable dynamics and fully chaotic dynamics with violated ${\mathcal T}$-invariance, and derive a Wigner-surmise like analytical expression for the corresponding nearest-neighbor spacing distribution. We propose a procedure involving this result and those for the RP model to determine the size of ${\mathcal T}$-invariance violation and chaoticity and validate it employing the experimental eigenfrequency spectra.

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

Abstract: We report on the theoretical and experimental investigations of the transition of a typical quantum system with mixed regular-integrable classical dynamics to one with violated time-reversal (${\mathcal T}$) invariance. The measurements are performed with a flat superconducting microwave resonator with circular shape in which chaoticity is induced by using either long antennas or inserting two circular disks into the cavity, and by magnetizing a ferrite disk placed at its center, which leads to violation of ${\mathcal T}$ invariance. We propose an extension of the Rosenzweig-Porter (RP) model, which interpolates between mixed regular-chaotic instead of integrable dynamics and fully chaotic dynamics with violated ${\mathcal T}$-invariance, and derive a Wigner-surmise like analytical expression for the corresponding nearest-neighbor spacing distribution. We propose a procedure involving this result and those for the RP model to determine the size of ${\mathcal T}$-invariance violation and chaoticity and validate it employing the experimental eigenfrequency spectra.

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

中图分类号: (Quantum chaos; semiclassical methods)

05.45.Mt

03.65.Sq (Semiclassical theories and applications) 41.20.Jb (Electromagnetic wave propagation; radiowave propagation) 05.45.Gg (Control of chaos, applications of chaos)

Xiaodong Zhang(张晓东), Jiongning Che(车炯宁), and Barbara Dietz. Experimental test of an extension of the Rosenzweig-Porter model to mixed integrable-chaotic systems experiencing time-reversal invariance violation[J]. 中国物理B, 2024, 33(12): 120501-120501.

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Experimental test of an extension of the Rosenzweig-Porter model to mixed integrable-chaotic systems experiencing time-reversal invariance violation

Experimental test of an extension of the Rosenzweig-Porter model to mixed integrable-chaotic systems experiencing time-reversal invariance violation

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