Richard Berkovits

The distribution of persistent currents in interacting 2D disordered cylinders

Abstract The distribution of persistent currents of small disordered 2D cylinders are calculated by an exact numerical diagonalization of a tight-binding interacting model Hamiltonian. The distribution is strongly influenced by the strength of the electron-electron (e-e) interactions. For strong e-e interactions there is almost no probability of measuring persistent currents in the direction opposite to the average current.

ABSENCE OF BIMODAL PEAK SPACING DISTRIBUTION IN THE COULOMB BLOCKADE REGIME

Using exact diagonalization numerical methods, as well as analytical arguments, we show that for the typical electron densities in chaotic and disordered dots the peak spacing distribution is not bimodal, but rather Gaussian. This is in agreement with the experimental observations. We attribute this behavior to the tendency of an even number of electrons to gain on-site interaction energy by removing the spin degeneracy. Thus, the dot is predicted to show a non trivial electron number dependent spin polarization. Experimental test of this hypothesis based on the spin polarization measurements are proposed.

Are the phases in the Anderson model long-range correlated?

We investigate the local cumulative phases at single sites of the lattice for time-dependent wave functions in the Anderson model in d=2 and 3. In addition to a local linear trend, the phases exhibit some fluctuations. We study the time correlations of these fluctuations using detrended fluctuation analysis. Our results suggest that the phase fluctuations are long-range correlated, decaying as a power law with time. It seems that the exponent depends on the degree of disorder. In d=3, close to the critical disorder wc=16.5, the correlation exponent exhibits a maximum value of α≈0.6 which is significantly above random fluctuations (α=0.5).

SPECTRAL STATISTICS NEAR THE QUANTUM PERCOLATION THRESHOLD

The statistical properties of spectra of a three-dimensional quantum bond percolation system is studied in the vicinity of the metal insulator transition. In order to avoid the influence of small clusters, only regions of the spectra in which the density of states is rather smooth are analyzed. Using finite size scaling hypothesis, the critical quantum probability for bond occupation is found to be

Resistance distribution in the hopping percolation model

p_q=0.33\pm.01

Localization transition on complex networks via spectral statistics

while the critical exponent for the divergence of the localization length is estimated as

Propagation of waves through a slab near the Anderson transition: a local scaling approach

\nu=1.35\pm.10

Interacting electrons in disordered potentials: Conductance versus persistent currents.

. This later figure is consistent with the one found within the universality class of the standard Anderson model.

Entanglement entropy in a one-dimensional disordered interacting system: the role of localization.

We study the distribution function P (rho) of the effective resistance rho in two- and three-dimensional random resistor networks of linear size L in the hopping percolation model. In this model each bond has a conductivity taken from an exponential form sigma proportional to exp (-kappar) , where kappa is a measure of disorder and r is a random number, 0< or = r < or =1 . We find that in both the usual strong-disorder regime L/ kappa(nu) >1 (not sensitive to removal of any single bond) and the extreme-disorder regime L/ kappa(nu) <1 (very sensitive to such a removal) the distribution depends only on L/kappa(nu) and can be well approximated by a log-normal function with dispersion b kappa(nu) /L , where b is a coefficient which depends on the type of lattice, and nu is the correlation critical exponent.

Discrete charging of a quantum dot strongly coupled to external leads

The spectral statistics of complex networks are numerically studied. The features of the Anderson metal-insulator transition are found to be similar for a wide range of different networks. A metal-insulator transition as a function of the disorder can be observed for different classes of complex networks for which the average connectivity is small. The critical index of the transition corresponds to the mean field expectation. When the connectivity is higher, the amount of disorder needed to reach a certain degree of localization is proportional to the average connectivity, though a precise transition cannot be identified. The absence of a clear transition at high connectivity is probably due to the very compact structure of the highly connected networks, resulting in a small diameter even for a large number of sites.