Distribution of the Ratio of Consecutive Level Spacings in Random Matrix Ensembles

2012/12/21 by Y. Y. Atas, E. Bogomolny, Olivier Giraud +3 · 9 citations
Mathematics · Physics and Astronomy · #Asymptotic distribution #Cold Atom Physics and Bose-Einstein Condensates #Distribution (mathematics) #Lattice (music) #Limit (mathematics) #Materials science #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Random matrix #Ratio distribution #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP

paper · pdf · doi:10.1103/physrevlett.110.084101

published as Phys. Rev. Lett. 110, 084101 (2013) · 5 pages, 4 figures

arxiv created 2012/12/21 · openalex publication_date 2013/02/21 · arxiv updated 2013/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body problems, as, contrary to the standard level spacing distributions, it does not depend on the local density of states. Our Wigner-like surmises are shown to be very accurate when compared to numerics and exact calculations in the large matrix size limit. Quantitative improvements are found through a polynomial expansion. Examples from a quantum many-body lattice model and from zeros of the Riemann zeta function are presented.

Citations

• Random Matrix Theories in Quantum Physics: Common Concepts
• Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
• Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E 8 Symmetry
• Random matrix theory
• Random-matrix physics: spectrum and strength fluctuations
• Zeros of principal L-functions and random matrix theory
• Localization of interacting fermions at high temperature
• An Attempt to Calculate the Number of Energy Levels of a Heavy Nucleus
• Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws
• Random Matrix Theory and ζ(1/2+ it)
• Statistical properties of the spectrum of the extended Bose–Hubbard model
• Level clustering in the regular spectrum
• On the numerical evaluation of Fredholm determinants

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• Observation of Strong and Weak Thermalization in a Superconducting Quantum Processor

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