TL;DR
This paper extends the analytical understanding of spacing ratio distributions in mixed quantum systems by combining integrable and chaotic blocks, validated through numerical simulations of key models.
Contribution
It introduces an analytical derivation of the spacing ratio distribution for mixed systems using a Rosenzweig-Porter type approach, bridging integrable and chaotic spectral analysis.
Findings
Analytical distribution derived for mixed systems.
Numerical confirmation in quantum kicked rotor.
Numerical confirmation in Hénon-Heiles system.
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 H\'enon-Heiles system.
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Taxonomy
TopicsRandom lasers and scattering media · Theoretical and Computational Physics · Neural dynamics and brain function