报告人：Marko Robnik 教授（马里博尔大学）

报告题目：Semiclassical behaviour of eigenstates in mixed-type systems

报告时间：2025年10月27日 下午15:00

报告地点：理工楼1201

联系人：黄亮

报告摘要：

I shall present a vast phenomenological evidence for the semiclassical behaviour of eigenstates in mixed-type (generic) quantum systems, by studying the Wigner and Husimi functions. Generally speaking we observe purely chaotic, purely regular and mixed-type states. However, in the semiclassical limit the relative fraction of mixedtype states decays as a power law as a function of the effective Planck constant, with exponent around −0.3 [1-5]. This is entirely in agreement with the Principle of Uniform Semiclassical Condensation (PUSC) of Wigner functions and/or Husimi functions (in the quantum phase space) [6]. The eigenstates can be categorized by means of the overlap index M in the phase space: for purely regular states M = −1, for purely chaotic states M = +1, while for the mixed-type states −1 < M < 1 [7]. I shall present the evidence that after the separation of chaotic states around M ≈ +1 these states can be dynamically localized. Then, their level spacing distribution is well described by the Brody distribution, and their localization measures satisfy the beta distribution. In the ultimate semiclassical limit the localization effects also disappear, and the GOE/GUE behaviour for the chaotic eigenstates is observed, while overall the Berry-Robnik picture [8] applies. These empirical findings are strongly corroborated by the very recent studies of banded random matrices [9].

References

[1] Cˇ. Lozej, D. Lukman and M. Robnik, Physical Review E. 106 (2022) 054203.

[2] Qian Wang and M. Robnik, Physical Review E. 108 (2023) 054217.  

[3] Qian Wang and M. Robnik, Physical Review E 109 (2024) 024225.  

[4] Hua Yan, Qian Wang and M. Robnik, Physical Review E 110 (2024) 064222.

[5] Hua Yan and M. Robnik, Physical Review E 109 (2024) 054211.  

[6] M. Robnik, Nonlinear Phenomena in Complex Systems 1 (1998) 1-22.

[7] B. Batisti´c and M. Robnik J. Phys. A: Math. Theor. 46 (2013) 315102.

[8] M.V. Berry and M. Robnik J. Phys. A: Math. Gen. 17 (1984) 2413-2421.  

[9] Hua Yan and M. Robnik, Physical Review E (2025) in preparation.

个人简介：

Marko Robnik, the founder (1990) and director of CAMTP - Center for Applied Mathematics and Theoretical Physics, University of Maribor, Slovenia, graduated with a degree in Physics at the University of Ljubljana, Slovenia, in 1978, and a Ph.D. degree at the University of Bonn, Germany, in 1981. He has organized and co-organized more than 65 world-class international conferences. Robnik has published 143 original research papers in various branches of theoretical physics, predominantly in nonlinear dynamics in classical and quantum chaos, and is one of the pioneers in quantum chaos. He has (co)edited several books and proceedings of various schools, most notably for series of world-class international summer schools including Let’s Face Chaos through Nonlinear Dynamics, held in Maribor, under his direction. He currently has an h-index of 43 and more than 6581 citations (Google Scholar). He has been a member of the European Academy of Sciences and Arts (Salzburg) since 2012. Robnik was also awarded the State Prize for Scientific Research of the Republic of Slovenia (the highest award in Slovenia for scientific work) in 1997. In 2025 he was awarded Blinc Prize for his life opus, for his scientific research, organizational and pedagogical work, which is the highest award in physics in Slovenia.