On the generalized dimensions of multifractal eigenstates

摘要: Recently, based on heuristic arguments, it was conjectured that an intimate relation exists between any multifractal dimensions, Dq and , of the eigenstates critical random matrix ensembles: 1 ⩽ q, q′ ⩽ 2. Here, we verify this by extensive numerical calculations ensembles extend its applicability to q < 1/2, but also deterministic models producing generic structures. We demonstrate, for scattering version power-law banded model at criticality, scaling exponents σq inverse moments Wigner delay times, where N is linear size system, are related level compressibility χ as σq ≈ q (1 − χ)[1 + qχ]−1 a limited range q, thus providing way probe correlations means experiments.