Eigenfunction entropy and spectral compressibility for critical random matrix ensembles

E. Bogomolny 1, O. Giraud 1

Physical Review Letters 106 (2011) 044101

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.

  • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud