Contrary to conventional wisdom, level repulsion in semiclassical spectrum is not just a feature of classically chaotic systems, but classically integrable systems as well. While in chaotic systems level repulsion develops on a scale of the mean level spacing, regardless of location in the spectrum, in integrable systems it develops on a much longer scale - geometric mean of the mean level spacing and the running energy in the spectrum. We show that at this scale level correlations in integrable systems have a universal dependence on level separation, as well as discuss their exact form at any scale. These correlations have dramatic consequences, including deviations from Poissonian statistics in the nearest level spacing distribution and persistent oscillations of level number variance as a function of the interval width. We illustrate our findings on two models - a rectangular infinite well and a modified Kepler problem - that serve as generic types of hard-wall billiards and potential problems. Our theory is based on the concept of parametric averaging, which allows for a statistical ensemble of integrable systems at a given spectral location (running energy).
Multi-mode input-output model for cavity magnonics: phase-resolved control of level repulsion, level attraction, and nonreciprocal transmission
kwan-tek；IMT Atlantique, Lab-STICC, UMR CNRS 6285（IMT大西洋学院，Lab-STICC，CNRS联合研究实验室6285）；Quantum Technologies and Dark Matter Labs, Department of Physics, University of Western Australia（西澳大利亚大学物理系量子技术与暗物质实验室）
Theory of the quantal level statistics of classically integrable system, developed by Makino et al. in order to investigate the non-Poissonian behaviors of level-spacing distribution (LSD) and level-number variance (LNV)\cite{MT03,MMT09}, is successfully extended to the study of $E(K,L)$ function which constitutes a fundamental measure to determine most statistical observables of quantal levels in addition to LSD and LNV. In the theory of Makino et al., the eigenenergy level is regarded as a superposition of infinitely many components whose formation is supported by the Berry-Robnik approach i…
Cavity-magnon polaritons (CMPs) are the associated quasiparticles of the hybridization between cavity photons and magnons in a magnetic sample placed in a microwave resonator. In the strong coupling regime, where the macroscopic coupling strength exceeds the individual dissipation, there is a coherent exchange of information. This renders CMPs as promising candidates for future applications such as in information processing. Recent advances on the study of the CMP now allow not only for creation of CMPs on demand, but also for tuning of the coupling strength - this can be thought of as enhanci…
For a Landau-Zener transition in a two-level system, the probability for a particle, initially in the first level, to survive the transition and to remain in the first level, does not depend on whether or not the second level is broadened [V. M. Akulin and W. P. Schleicht, Phys. Rev. A {\bf 46}, 4110 (1992)]. In other words, the seminal Landau-Zener result applies regardless of the broadening of the second level. The same question for the multistate Landau-Zener transition is addressed in the present paper. While for integrable multistate models, where the transition does not involve interfere…
We characterize some of the distinctive hallmarks of magnon-magnon interaction mediated by the intracavity field of a microwave cavity, along with their testable ramifications. In general, we foreground two widely dissimilar parameter domains that bring forth the contrasting possibilities of level splitting and level crossing. The former is observed in the regime of strong magnon-photon couplings, particularly when the three modes bear comparable relaxation rates. This character is marked by the appearance of three distinguishable and non-converging polariton branches in the spectral response …
Matrix models showing chaotic-integrable transition in the spectral statistics are important for understanding Many Body Localization (MBL) in physical systems. One such example is the $β$-ensemble, known for its structural simplicity. However, eigenvector properties of $β$-ensemble remain largely unexplored, despite energy level correlations being thoroughly studied. In this work we numerically study the eigenvector properties of $β$-ensemble and find that the Anderson transition occurs at $γ= 1$ and ergodicity breaks down at $γ= 0$ if we express the repulsion parameter as $β= N^{-γ}$. Thus o…
We discuss solvable multistate Landau-Zener (MLZ) models whose Hamiltonians have commuting partner operators with $\sim 1/τ$-time-dependent parameters. Many already known solvable MLZ models belong precisely to this class. We derive the integrability conditions on the parameters of such commuting operators, and demonstrate how to use such conditions in order to derive new solvable cases. We show that MLZ models from this class must contain bands of parallel diabatic energy levels. The structure of the scattering matrix and other properties are found to be the same as in the previously discusse…
The article provides a framework to solve linear differential equations based on partial commutativity which is introduced by means of the Fedorov theorem. The framework is applied to specific types of three-level and four-level quantum systems. The efficiency of the method is evaluated and discussed. The Fedorov theorem appears to answer the need for methods which allow to study dynamical maps corresponding with time-dependent generators. By applying this method, one can investigate countless examples of dissipative systems such that the relaxation rates depend on time.
