Eigenfunction entropy and spectral compressibility for critical random matrix ensembles

Nonlinear Sciences – Chaotic Dynamics

Scientific paper

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4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.106.044101

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.

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