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