We review the development of random-matrix theory (RMT) during the last fifteen years. We
emphasize both the theoretical aspects, and the application of the theory to a number of …

The article reviews recent developments in the theory of fluctuations and correlations of
energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various …

This review is intended to give a pedagogical and unified view on the subject of the statistics
and scaling of physical quantities in disordered electron systems at very low temperatures …

Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in
the Anderson model on random regular graphs (RRG) are studied. We consider the critical …

In this paper, we suggest an extension of the Rosenzweig-Porter (RP) model, the LN-RP
model, in which the off-diagonal matrix elements have a wide, log-normal distribution. We …

arxiv:cond-mat/0609580v1 [cond-mat.mes-hall] 22 Sep 2006 Page 1 arxiv:cond-mat/0609580v1
[cond-mat.mes-hall] 22 Sep 2006 submitted to acta physica slovaca 1– 123 NUMERICAL …

In this paper we present a thorough study of transport, spectral, and wave-function
properties at the Anderson localization critical point in spatial dimensions d= 3, 4, 5, 6. Our …

Level statistics of systems that undergo many-body localization transition are studied. An
analysis of the gap ratio statistics from the perspective of inter-and intrasample randomness …

Why life persists at the edge of chaos is a question at the very heart of evolution. Here we
show that molecules taking part in biochemical processes from small molecules to proteins …

The statistics of energy levels for a disordered conductor are considered in the critical
energy window near the mobility edge. It is shown that, if the critical wave functions are …