SPECTRAL CORRELATIONS IN DISORDERED ELECTRONIC SYSTEMS: CROSSOVER FROM METAL TO INSULATOR REGIME

We use the semiclassical approach combined with the scaling results for the diffusion coefficient to consider the two-level correlation function $R(\varepsilon)$ for a disordered electron system in the crossover region, characterized by the appearance of a macroscopic correlation or localization length, $\xi$, that diverges at the metal-insulator transition. We show new critical statistics, characterized by a nontrivial asymptotic behavior of $R(\varepsilon)$, to emerge on both sides of the transition at higher energies, and to expand to all energies larger than mean level spacing when $\xi$ exceeds the system size.Comment: 4 pages,1 figure, in self-ectracting uuencoded gz-compressed file to be published in Phys. Rev. Letters; REVTeX source file is available upon reques

Multiphoton Processes in Driven Mesoscopic Systems

We study the statistics of multi-photon absorption/emission processes in a mesoscopic ring threaded by an harmonic time-dependent flux $\Phi(t)$. For this sake, we demonstrate a useful analogy between the Keldysh quantum kinetic equation for the electrons distribution function and a Continuous Time Random Walk in energy space with corrections due to interference effects. Studying the probability to absorb/emit $n$ quanta $\hbar\omega$ per scattering event, we explore the crossover between ultra-quantum/low-intensity limit and quasi-classical/high-intensity regime, and the role of multiphoton processes in driving it.Comment: 6 pages, 5 figures, extended versio

One-dimensional Anderson Localization: Devil's staircase of Statistical Anomalies

The statistics of wavefunctions in the one-dimensional (1d) Anderson model of localization is considered. It is shown that at any energy that corresponds to a rational filling factor f=p/q there is a statistical anomaly which is seen in expansion of the generating function (GF) to the order (q-2) in the disorder parameter. We study in detail the principle anomaly at $f=1/2$ that appears in the leading order. The transfer-matrix equation of the Fokker-Planck type with a two-dimensional internal space is derived for GF. It is shown that the zero-mode variant of this equation is integrable and a solution for the generating function is found in the thermodynamic limit.Comment: 4 pages RevTex, 1 pictur

Energy level statistics of a critical random matrix ensemble

We study level statistics of a critical random matrix ensemble of a power-law banded complex Hermitean matrices. We compute numerically the level compressibility via the level number variance and compare it with the analytical formula for the exactly solvable model of Moshe, Neuberger and Shapiro.Comment: 8 pages, 3 figure