Multifractal properties of critical eigenstates in two-dimensional systems with symplectic symmetry

The multifractal properties of electronic eigenstates at the metal-insulator transition of a two-dimensional disordered tight-binding model with spin-orbit interaction are investigated numerically. The correlation dimensions of the spectral measure $\widetilde{D}_{2}$ and of the fractal eigenstate $D_{2}$ are calculated and shown to be related by $D_{2}=2\widetilde{D}_{2}$. The exponent $\eta=0.35\pm 0.05$ describing the energy correlations of the critical eigenstates is found to satisfy the relation $\eta=2-D_{2}$.Comment: 6 pages RevTeX; 3 uuencoded, gzipped ps-figures to appear in J. Phys. Condensed Matte

Does Use of Gypsum Improve Soil Structure in Kentucky?

Gypsum is sometimes recommended as a soil amendment in order to improve structure. Although this practice is often used for reclamation of sodic soils (Na+ saturated) in the western USA, it\u27s value in improving soil structure in Kentucky is questionable. The following discussion explains way

Two Interacting Electrons in a Quasiperiodic Chain

We study numerically the effect of on-site Hubbard interaction U between two electrons in the quasiperiodic Harper's equation. In the periodic chain limit by mapping the problem to that of one electron in two dimensions with a diagonal line of impurities of strength U we demonstrate a band of resonance two particle pairing states starting from E=U. In the ballistic (metallic) regime we show explicitly interaction-assisted extended pairing states and multifractal pairing states in the diffusive (critical) regime. We also obtain localized pairing states in the gaps and the created subband due to U, whose number increases when going to the localized regime, which are responsible for reducing the velocity and the diffusion coefficient in the qualitatively similar to the non-interacting case ballistic and diffusive dynamics. In the localized regime we find propagation enhancement for small U and stronger localization for larger U, as in disordered systems.Comment: 14 pages Revtex file, 8 figures (split into 19 jpg figures). (postscript versions of the jpg figures are also available upon request) submitted to PR

Delocalization and spin-wave dynamics in ferromagnetic chains with long-range correlated random exchange

We study the one-dimensional quantum Heisenberg ferromagnet with exchange couplings exhibiting long-range correlated disorder with power spectrum proportional to $1/k^{\alpha}$, where $k$ is the wave-vector of the modulations on the random coupling landscape. By using renormalization group, integration of the equations of motion and exact diagonalization, we compute the spin-wave localization length and the mean-square displacement of the wave-packet. We find that, associated with the emergence of extended spin-waves in the low-energy region for $\alpha > 1$, the wave-packet mean-square displacement changes from a long-time super-diffusive behavior for $\alpha <1$ to a long-time ballistic behavior for $\alpha > 1$. At the vicinity of $\alpha =1$, the mobility edge separating the extended and localized phases is shown to scale with the degree of correlation as $E_c\propto (\alpha -1)^{1/3}$.Comment: PRB to appea

The Effect of Oil Well Brines on Agricultural Fields and Water

What is Brine and Where Does it Come From? Brine is the salty water trapped in rock formations associated with oil and gas deposits. It consists mostly of sodium chloride but can also contain other things such as organics, bromide, some heavy metals and boron. Its source as a pollutant is usually oil stripper wells which produce less than 10 barrels of oil per day with typically a 10:1 ratio of brine to oil. Such wells are distributed throughout Kentucky and are often located on farmland. In some cases, brine rises to the land surface even where no oil wells are present

Predicting Potential Aluminum Contamination of Surface and Ground Waters from Acid Sulfate Enriched Drainages Emanating from Low Neutralization Capacity Watersheds

The composition of soil solutions and surface waters emanating from unreclaimed, or partially reclaimed, strip-mined watersheds with low buffering capacity in Kentucky were compared with soil solution compositions of unaffected strata in the watershed. The data suggests that almost 20 years after mining, most soil solutions and surface waters of the disturbed areas still contain high levels of undissolved Al, controlled primarily by the solubilities of a jurbanite-like material (upper limit) and alunite (lower limit)

Critical regime of two dimensional Ando model: relation between critical conductance and fractal dimension of electronic eigenstates

The critical two-terminal conductance $g_c$ and the spatial fluctuations of critical eigenstates are investigated for a disordered two dimensional model of non-interacting electrons subject to spin-orbit scattering (Ando model). For square samples, we verify numerically the relation $\sigma_c=1/[2\pi(2-D(1))] e^2/h$ between critical conductivity $\sigma_c=g_c=(1.42\pm 0.005) e^2/h$ and the fractal information dimension of the electron wave function, $D(1)=1.889\pm 0.001$. Through a detailed numerical scaling analysis of the two-terminal conductance we also estimate the critical exponent $\nu=2.80\pm 0.04$ that governs the quantum phase transition.Comment: IOP Latex, 7 figure

Predicting Potential Aluminum Contamination of Surface and Ground Waters from Acid Sulfate Enriched Drainages Emanating from Low Neutralization Capacity Watersheds

The composition of soil solutions and surface waters emanating from unreclaimed, or partially reclaimed, strip-mined watersheds with low buffering capacity in Kentucky were compared with soil solution compositions of unaffected strata in the watershed. The data suggest that almost 20 years after mining, most soil solutions and surface waters of the disturbed areas still contain high levels of dissolved Al, controlled primarily by the solubilities of a jurbanite-like mineral (upper limit) and alunite (lower limit). Soluble Al in solutions of undisturbed areas was consistent with the solubility of kaolinite or gibbsite. The absence of jurbanite x-ray diffraction peaks suggested the presence of an amorphous mineral or one stoichiometrically similar to jurbanite. Despite greater residence times for soil solutions as compared to surface waters, their compositional differences were insignificant. The control of soluble AL by basic aluminum sulfate minerals was not affected by the variable mineralogical and textural composition of soil and geologic strata in the watershed. Apparently, this is the result of low buffering capacity. At pH 4, pH and sulfate activities can be used to accurately predict the levels of soluble Al3+ in surface and ground waters of the watersheds. Similar predictions from pH and SO2-/4 activities can also be made for dissolved Fe3+ levels, supporting the stoichiometry but a much higher solubility than that of jarosite

The Anderson Transition in Two-Dimensional Systems with Spin-Orbit Coupling

We report a numerical investigation of the Anderson transition in two-dimensional systems with spin-orbit coupling. An accurate estimate of the critical exponent $\nu$ for the divergence of the localization length in this universality class has to our knowledge not been reported in the literature. Here we analyse the SU(2) model. We find that for this model corrections to scaling due to irrelevant scaling variables may be neglected permitting an accurate estimate of the exponent $\nu=2.73 \pm 0.02$

Anderson transition in three-dimensional disordered systems with symplectic symmetry

The Anderson transition in a 3D system with symplectic symmetry is investigated numerically. From a one-parameter scaling analysis the critical exponent $\nu$ of the localization length is extracted and estimated to be $\nu = 1.3 \pm 0.2$. The level statistics at the critical point are also analyzed and shown to be scale independent. The form of the energy level spacing distribution $P(s)$ at the critical point is found to be different from that for the orthogonal ensemble suggesting that the breaking of spin rotation symmetry is relevant at the critical point.Comment: 4 pages, revtex, to appear in Physical Review Letters. 3 figures available on request either by fax or normal mail from [email protected] or [email protected]