Spacing ratios in mixed-type systems
arXiv:2501.12874 · doi:10.1103/PhysRevE.111.054213
Abstract
The distribution of the consecutive level-spacing ratio is now widely used as a tool to distinguish integrable from chaotic quantum spectra, mostly due to its avoiding of the numerical spectral unfolding. Similar to the use of the Rosenzweig-Porter approach to obtain the Berry-Robnik distribution of level-spacings in mixed-type systems, in this work we extend this approach to derive analytically the distribution of spacing ratios, for random matrices comprised of independent integrable blocks and chaotic blocks. We have numerically confirmed this analytical result using random matrix theory in paradigmatic models such as the quantum kicked rotor and the Hénon-Heiles system.
References in corpus (18)
- Localization of interacting fermions at high temperature
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
- Geometrical structure of Laplacian eigenfunctions
- Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos
- Periodic-orbit theory of universal level correlations in quantum chaos
- 100 years of Weyl's law
- Probing symmetries of quantum many-body systems through gap ratio statistics
- Hearing shapes of drums - mathematical and physical aspects of isospectrality
- Observation of high-order quantum resonances in the kicked rotor
- Theory of localization and resonance phenomena in the quantum kicked rotor
- Berry-Robnik level statistics in a smooth billiard system
- Statistical properties of the localization measure of chaotic eigenstates and the spectral statistics in a mixed-type billiard
- Effects of stickiness in the classical and quantum ergodic lemon billiard
- Stickiness in generic low-dimensional Hamiltonian systems: A recurrence-time statistics approach
- The distribution of localization measures of chaotic eigenstates in the stadium billiard
- The level repulsion exponent of localized chaotic eigenstates as a function of the classical transport time scales in the stadium billiard
- On the Spectrum of the Resonant Quantum Kicked Rotor