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On the Generalized Dimensions of Multifractal Eigenstates by Mendez-Bermudez, J. A.; Alcazar-Lopez, A.; Varga, Imre is a scholarly article available to read on EtoBox.

What is On the Generalized Dimensions of Multifractal Eigenstates about?

Recently, based on heuristic arguments, it was conjectured that an intimate relation exists between any multifractal dimensions, $D_q$ and $D_{q'}$, of the eigenstates of critical random matrix ensembles: $D_{q'} \approx qD_q[q'+(q-q')D_q]^{-1}$, $1\le q, q' \le 2$. Here, we verify this relation by extensive numerical calculations on critical random matrix ensembles and extend its applicability to $q<1/2$ but also to deterministic models producing multifractal eigenstates and to generic multifractal structures. 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.

Author

Mendez-Bermudez, J. A.; Alcazar-Lopez, A.; Varga, Imre

Published

2013

Language

EN