## On the generalized dimensions of multifractal eigenstates    [PDF]

J. A. Mendez-Bermudez, A. Alcazar-Lopez, Imre Varga
Recently [Europhys. Lett. {\bf 98}, 37006 (2012)], based on heuristic arguments, it was conjectured that an intimate relation exists between the eigenfunction multifractal dimensions $D_q$ of the eigenstates of critical random matrix ensembles $D_{q'} \approx qD_q[q'+(q-q')D_q]^{-1}$, $1\le q \le 2$. Here, we verify this relation by extensive numerical calculations on critical random matrix ensembles and extend its applicability to $q<1/2$ and also to deterministic models producing multifractal eigenstates. We also demonstrate, for the scattering version of the power-law banded random matrix model at criticality, that the scaling exponents $\sigma_q$ of the inverse moments of Wigner delay times, $\bra \tau_{\tbox W}^{-q} \ket \propto N^{-\sigma_q}$ where $N$ is the linear size of the system, are related to the level compressibility $\chi$ as $\sigma_q\approx q(1-\chi)[1+q\chi]^{-1}$ for a limited range of $q$; thus providing a way to probe level correlations by means of scattering experiments.
View original: http://arxiv.org/abs/1303.5665