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Eigenfunction entropy and spectral compressibility for critical random matrix ensembles

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arxiv 1011.3686 v1 pith:OUNDI6AQ submitted 2010-11-16 nlin.CD cond-mat.stat-mech

E. Bogomolny , O. Giraud This is my paper · ORCID
classification nlin.CDcond-mat.stat-mech
keywords compressibilitycriticalmatrixrandomspectralargumentscertainconjecture
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Based on numerical and perturbation series arguments we conjecture that for certain critical random matrix models the information dimension of eigenfunctions D_1 and the spectral compressibility chi are related by the simple equation chi+D_1/d=1, where d is the system dimensionality.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Crystalline Spectral Form Factors

    quant-ph 2025-12 conditional novelty 6.0 of 10

    Strong level repulsion produces damped crystalline oscillations of the spectral form factor, with a Debye-Waller suppression, a new plateau time scale t* ≈ t_H sqrt(β/4), and predictable derivative singularities.

  2. How Random Are Ergodic Eigenstates of the Ultrametric Random Matrices and the Quantum Sun Model?

    quant-ph 2025-01 conditional novelty 5.0 of 10

    Extreme value statistics of Schmidt eigenvalues reveal deviations from Wishart behavior in ergodic eigenstates of ultrametric random matrices and the Quantum Sun model.

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