Distribution of the Ratio of Consecutive Level Spacings for Different Symmetries and Degrees of Chaos
arXiv:1910.01434 · doi:10.1103/PhysRevE.101.022222
Abstract
Theoretical expressions for the distribution of the ratio of consecutive level spacings for quantum systems with transiting dynamics remain unknown. We propose a family of one-parameter distributions , where is a generalized Dyson index, that describes the eigenlevel statistics of a quantum system characterized by different symmetries and degrees of chaos. We show that this crossover strongly depends on the specific properties of each model, and thus the reduction of such a family to a universal formula, albeit desirable, is not possible. We use the information entropy as a criterion to suggest particular ansatzs for different transitions, with a negligible associated error in the limits corresponding to standard random ensembles.
arXiv comment11 pages, 9 figures, 3 tables. Accepted preprint; to appear in Phys. Rev. E
References in corpus (40)
- Many-Body Physics with Ultracold Gases
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Localization of interacting fermions at high temperature
- Many-body localization edge in the random-field Heisenberg chain
- Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
- Matrix Models for Beta Ensembles
- Many-Body Localization in a Quasiperiodic System
- Exactly solvable Richardson-Gaudin models for many-body quantum systems
- Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
- Extended slow dynamical regime close to the many-body localization transition
- Spectral statistics across the many-body localization transition
- Exactly-Solvable Models Derived from a Generalized Gaudin Algebra
- Periodic-Orbit Theory of Level Correlations
- Integrability of a disordered Heisenberg spin-1/2 chain
- Misleading signatures of quantum chaos
- Statistical properties of the spectrum the extended Bose-Hubbard model
- Statistics of Atmospheric Correlations
- Joint probability densities of level spacing ratios in random matrices
- Universal spectral statistics in quantum graphs
- Model of level statistics for disordered interacting quantum many-body systems
- Random Matrix Ensemble for the Level Statistics of Many-Body Localization
- Universal Quantum Graphs
- Higher order spacing ratios in random matrix theory and complex quantum systems
- Large Scale Cross-Correlations in Internet Traffic
- Poisson to GOE transition in the distribution of the ratio of consecutive level spacings
- Eigenvalues of Hermite and Laguerre ensembles: Large Beta Asymptotics
- Many-Body Physics and Quantum Chaos
- Entangling many-body bound states with propagative modes in Bose-Hubbard systems
- Universal power law in crossover from integrability to quantum chaos
- Discrete disorder models for many-body localization
- Probability Distribution of the Ratio of Consecutive Level Spacings in Interacting Particle Systems
- Nearest-neigbor spacing distributions of the beta-Hermite ensemble of random matrices
- Exact distribution of spacing ratios for random and localized states in quantum chaotic systems
- Distribution of the ratio of two consecutive level spacings in orthogonal to unitary crossover ensembles
- Scaling in the eigenvalue fluctuations of the empirical correlation matrices
- Elliptic Gaudin models and elliptic KZ Equations
- Semiclassical Theory for Universality in Quantum Chaos with Symmetry Crossover
- Stringent Test on Power Spectrum of Quantum Integrable and Chaotic Systems
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- Spectral Crossovers and Universality in Quantum Spin-chains Coupled to Random Fields
- Power-law decay of the fraction of the mixed eigenstates in kicked top model with mixed-type classical phase space
- Mixed eigenstates in the Dicke model: Statistics and power-law decay of the relative proportion in the semiclassical limit
- Spectral statistics of multi-parametric Gaussian ensembles with chiral symmetry
- Scaling of the Reduced Energy Spectrum of Random Matrix Ensemble
- Diagnosing First and Second Order Phase Transitions with Probes of Quantum Chaos
- Spectrum statistics in the integrable Lieb-Liniger model
- Higher-order gap ratios of singular values in open quantum systems
- Random Matrix Model for Eigenvalue Statistics in Random Spin Systems
- Spectral form factor and energy correlations in banded random matrices
- Chaos enhancement in large-spin chains
- Comment on 'Revisiting the phase transitions of the Dicke model'
- Suppressing chaos with mixed superconducting qubit devices
- Ordered Level Spacing Distribution in Embedded Random Matrix Ensembles
- Higher-Order Krylov State Complexity in Random Matrix Quenches
- A bipartite Sachdev-Ye-Kitaev model: Conformal limit and level statistics
- Limitations of SVD-Based Diagnostics for Non-Hermitian Many-Body Localization with Time-Reversal Symmetry
- Universal transition of spectral fluctuation in particle-hole symmetric system