Eigenfunction entropy and spectral compressibility for critical random matrix ensembles

E. Bogomolny (1) , O. Giraud (1)

1 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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.

Domaines: Dynamique Chaotique [nlin.CD]; Mécanique statistique [cond-mat.stat-mech]

E. Bogomolny, O. Giraud. Eigenfunction entropy and spectral compressibility for critical random matrix ensembles. Physical Review Letters, 2011, 106, pp.044101. ⟨10.1103/PhysRevLett.106.044101⟩. ⟨hal-00564300⟩