Scaling and the center of band anomaly in a one-dimensional Anderson model with diagonal disorder

We resolve the problem of the violation of single parameter scaling at the zero energy of the Anderson tight-binding model with diagonal disorder. It follows from the symmetry properties of the tight-binding Hamiltonian that this spectral point is in fact a boundary between two adjacent bands. The states in the vicinity of this energy behave similarly to states at other band boundaries, which are known to violate single parameter scaling.Comment: revised version, 4 pages, 2 figures, revte

Low density expansion for Lyapunov exponents

In some quasi-one-dimensional weakly disordered media, impurities are large and rare rather than small and dense. For an Anderson model with a low density of strong impurities, a perturbation theory in the impurity density is developed for the Lyapunov exponent and the density of states. The Lyapunov exponent grows linearly with the density. Anomalies of the Kappus-Wegner type appear for all rational quasi-momenta even in lowest order perturbation theory

1D quantum models with correlated disorder vs. classical oscillators with coloured noise

We perform an analytical study of the correspondence between a classical oscillator with frequency perturbed by a coloured noise and the one-dimensional Anderson-type model with correlated diagonal disorder. It is rigorously shown that localisation of electronic states in the quantum model corresponds to exponential divergence of nearby trajectories of the classical random oscillator. We discuss the relation between the localisation length for the quantum model and the rate of energy growth for the stochastic oscillator. Finally, we examine the problem of electron transmission through a finite disordered barrier by considering the evolution of the classical oscillator.Comment: 23 pages, LaTeX fil

Random Fibonacci Sequences

Solutions to the random Fibonacci recurrence x_{n+1}=x_{n} + or - Bx_{n-1} decrease (increase) exponentially, x_{n} = exp(lambda n), for sufficiently small (large) B. In the limits B --> 0 and B --> infinity, we expand the Lyapunov exponent lambda(B) in powers of B and B^{-1}, respectively. For the classical case of $\beta=1$ we obtain exact non-perturbative results. In particular, an invariant measure associated with Ricatti variable r_n=x_{n+1}/x_{n} is shown to exhibit plateaux around all rational.Comment: 11 Pages (Multi-Column); 3 EPS Figures ; Submitted to J. Phys.

Anderson localization as a parametric instability of the linear kicked oscillator

We rigorously analyse the correspondence between the one-dimensional standard Anderson model and a related classical system, the `kicked oscillator' with noisy frequency. We show that the Anderson localization corresponds to a parametric instability of the oscillator, with the localization length determined by an increment of the exponential growth of the energy. Analytical expression for a weak disorder is obtained, which is valid both inside the energy band and at the band edge.Comment: 7 pages, Revtex, no figures, submitted to Phys. Rev.

Scaling of the localization length in linear electronic and vibrational systems with long-range correlated disorder

The localization lengths of long-range correlated disordered chains are studied for electronic wavefunctions in the Anderson model and for vibrational states. A scaling theory close to the band edge is developed in the Anderson model and supported by numerical simulations. This scaling theory is mapped onto the vibrational case at small frequencies. It is shown that for small frequencies, unexpectateley the localization length is smaller for correlated than for uncorrelated chains.Comment: to be published in PRB, 4 pages, 2 Figure

Decay Rate Distributions of Disordered Slabs and Application to Random Lasers

We compute the distribution of the decay rates (also referred to as residues) of the eigenstates of a disordered slab from a numerical model. From the results of the numerical simulations, we are able to find simple analytical formulae that describe those results well. This is possible for samples both in the diffusive and in the localised regime. As example of a possible application, we investigate the lasing threshold of random lasers.Comment: 11 pages, 11 figure

Persistent Currents in Multichannel Interacting Systems

Persistent currents of disordered multichannel mesoscopic rings of spinless interacting fermions threaded by a magnetic flux are calculated using exact diagonalizations and self-consistent Hartree-Fock methods. The validity of the Hartree-Fock approximation is controled by a direct comparison with the exact results on small $4\times4$ clusters. For sufficiently large disorder (diffusive regime), the effect of repulsive interactions on the current distribution is to slightly decrease its width (mean square current) but to {\it increase} its mean value (mean current). This effect is stronger in the case of a long range repulsion. Our results suggest that the coupling between the chains is essential to understand the large currents observed experimentally.Comment: Revised version, uuencoded compressed file including fig

Tectonomagmatic Evolution of Southwestern Laurentia: Insights from Zircon U-Pb Geochronology and Hafnium Isotopic Composition of the Red Bluff Granite Suite, West Texas, USA

We provide laser ablation–multicollector–inductively coupled plasma–mass spectrometry (LA-MC-ICP-MS) and high-precision chemical abrasion–isotope dilution–thermal ionization mass spectrometry (CA-ID-TIMS) U-Pb ages and Hf isotopic compositions of zircons from the Red Bluff Granite Suite and mafic dikes in the Franklin Mountains of El Paso, Texas, USA. Granitoids exposed in the Franklin Mountains were previously divided into five magmatic stages based on cross-cutting relationships. Major and trace element compositions showed that these granitoids are ferroan, alkaline, and A2 type. Homogeneity in the whole-rock geochemistry suggests that the granite stages are genetically related and share similar petrogenetic histories. Weighted mean zircon 206Pb/238U dates from the older magmatic stage 1 alkali-feldspar quartz syenite and stage 2 alkali-feldspar granite are 1112.36 ± 0.35 and 1112.46 ± 0.37 Ma, respectively. The weighted mean εHf(t) values varying from +5.3 to +7.2 are similar to those of other regional ca. 1.1 Ga magmatic rocks throughout southwestern Laurentia. Geochemical characteristics, petrological modeling, and enriched Hf isotopic composition suggest fractional crystallization of a basaltic magma that was produced by melting of an enriched mantle reservoir. However, zircon inheritance ages of ca. 1.3 Ga and 1.26–1.15 Ga are consistent with a minor contribution from felsic crustal basement. Our data and regional geology are consistent with a post-collisional slab break-off that facilitated asthenospheric upwelling and partial melting of the enriched mantle, possibly subcontinental lithospheric mantle, extending from Llano Uplift, Texas, in the southeast to California to the northwest. Magma thus generated upon differentiation produced ferroan and A-type granitoids