Scaling of Level Statistics at the Disorder-Induced Metal-Insulator Transition

The distribution of energy level separations for lattices of sizes up to 28$\times$28$\times$28 sites is numerically calculated for the Anderson model. The results show one-parameter scaling. The size-independent universality of the critical level spacing distribution allows to detect with high precision the critical disorder $W_{c}=16.35$. The scaling properties yield the critical exponent, $\nu =1.45 \pm 0.08$, and the disorder dependence of the correlation length.Comment: 11 pages (RevTex), 3 figures included (tar-compressed and uuencoded using UUFILES), to appear in Phys.Rev. B 51 (Rapid Commun.

Spectral Correlations from the Metal to the Mobility Edge

We have studied numerically the spectral correlations in a metallic phase and at the metal-insulator transition. We have calculated directly the two-point correlation function of the density of states $R(s,s')$. In the metallic phase, it is well described by the Random Matrix Theory (RMT). For the first time, we also find numerically the diffusive corrections for the number variance $$ predicted by Al'tshuler and Shklovski\u{\i}. At the transition, at small energy scales, $R(s-s')$ starts linearly, with a slope larger than in a metal. At large separations $|s - s'| \gg 1$, it is found to decrease as a power law $R(s,s') \sim - c / |s -s'|^{2-\gamma}$ with $c \sim 0.041$ and $\gamma \sim 0.83$, in good agreement with recent microscopic predictions. At the transition, we have also calculated the form factor $\tilde K(t)$, Fourier transform of $R(s-s')$. At large $s$, the number variance contains two terms $= B ^\gamma + 2 \pi \tilde K(0) where$\tilde{K}(0)$is the limit of the form factor for$t \to 0$.Comment: 7 RevTex-pages, 10 figures. Submitted to PR

Unitary limit and quantum interference effect in disordered two-dimensional crystals with nearly half-filled bands

Based on the self-consistent $T$-matrix approximation, the quantum interference (QI) effect is studied with the diagrammatic technique in weakly-disordered two-dimensional crystals with nearly half-filled bands. In addition to the usual 0-mode cooperon and diffuson, there exist $\pi$-mode cooperon and diffuson in the unitary limit due to the particle-hole symmetry. The diffusive $\pi$-modes are gapped by the deviation from the exactly-nested Fermi surface. The conductivity diagrams with the gapped $\pi$-mode cooperon or diffuson are found to give rise to unconventional features of the QI effect. Besides the inelastic scattering, the thermal fluctuation is shown to be also an important dephasing mechanism in the QI processes related with the diffusive $\pi$-modes. In the proximity of the nesting case, a power-law anti-localization effect appears due to the $\pi$-mode diffuson. For large deviation from the nested Fermi surface, this anti-localization effect is suppressed, and the conductivity remains to have the usual logarithmic weak-localization correction contributed by the 0-mode cooperon. As a result, the dc conductivity in the unitary limit becomes a non-monotonic function of the temperature or the sample size, which is quite different from the prediction of the usual weak-localization theory.Comment: 21 pages, 4 figure

On Renyi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems

We discuss some properties of the generalized entropies, called Renyi entropies and their application to the case of continuous distributions. In particular it is shown that these measures of complexity can be divergent, however, their differences are free from these divergences thus enabling them to be good candidates for the description of the extension and the shape of continuous distributions. We apply this formalism to the projection of wave functions onto the coherent state basis, i.e. to the Husimi representation. We also show how the localization properties of the Husimi distribution on average can be reconstructed from its marginal distributions that are calculated in position and momentum space in the case when the phase space has no structure, i.e. no classical limit can be defined. Numerical simulations on a one dimensional disordered system corroborate our expectations.Comment: 8 pages with 2 embedded eps figures, RevTex4, AmsMath included, submitted to PR

Association Between Gestational Diabetes and Incident Maternal CKD: The Coronary Artery Risk Development in Young Adults (CARDIA) Study

Background Gestational diabetes mellitus (GDM) is associated with increased risk for diabetes mellitus, metabolic syndrome, and cardiovascular disease. We evaluated whether GDM is associated with incident chronic kidney disease (CKD), controlling for prepregnancy risk factors for both conditions. Study Design Prospective cohort. Setting & Participants Of 2,747 women (aged 18-30 years) enrolled in the Coronary Artery Risk Development in Young Adults (CARDIA) Study in 1985 to 86, we studied 820 who were nulliparous at enrollment, delivered at least 1 pregnancy longer than 20 weeks’ gestation, and had kidney function measurements during 25 years of follow-up. Predictor GDM was self-reported by women for each pregnancy. Outcomes CKD was defined as the development of estimated glomerular filtration rate (eGFR) < 60 mL/min/1.73 m2 or urine albumin-creatinine ratio ≥ 25 mg/g at any one CARDIA examination in years 10, 15, 20, or 25. Measurements HRs for developing CKD were estimated for women who developed GDM versus women without GDM using complementary log-log models, adjusting for prepregnancy age, systolic blood pressure, dyslipidemia, body mass index, smoking, education, eGFR, fasting glucose concentration, physical activity level (all measured at the CARDIA examination before the first pregnancy), race, and family history of diabetes. We explored for an interaction between race and GDM. Results During a mean follow-up of 20.8 years, 105 of 820 (12.8%) women developed CKD, predominantly increased urine albumin excretion (98 albuminuria only, 4 decreased eGFR only, and 3 both). There was evidence of a GDM-race interaction on CKD risk (P = 0.06). Among black women, the adjusted HR for CKD was 1.96 (95% CI, 1.04-3.67) in GDM compared with those without GDM. Among white women, the HR was 0.65 (95% CI, 0.23-1.83). Limitations Albuminuria was assessed by single untimed measurements of urine albumin and creatinine. Conclusions GDM is associated with the subsequent development of albuminuria among black women in CARDIA

Singularity free dilaton-driven cosmologies and pre-little-bang

There are no reasons why the singularity in the growth of the dilaton coupling should not be regularised, in a string cosmological context, by the presence of classical inhomogeneities. We discuss a class of inhomogeneous dilaton-driven models whose curvature invariants are all bounded and regular in time and space. We prove that the non-space-like geodesics of these models are all complete in the sense that none of them reaches infinity for a finite value of the affine parameter. We conclude that our examples represent truly singularity-free solutions of the low energy beta functions. We discuss some symmetries of the obtained solutions and we clarify their physical interpretation. We also give examples of solutions with spherical symmetry. In our scenario each physical quantity is everywhere defined in time and space, the big-bang singularity is replaced by a maximal curvature phase where the dilaton kinetic energy reaches its maximum. The maximal curvature is always smaller than one (in string units) and the coupling constant is also smaller than one and it grows between two regimes of constant dilaton, implying, together with the symmetries of the solutions, that higher genus and higher curvature corrections are negligible. We argue that our examples describe, in a string cosmological context, the occurrence of ``little bangs''(i.e. high curvature phases which never develop physical singularities). They also suggest the possibility of an unexplored ``pre-little-bang'' phase.Comment: 25 pages in LaTex style, 3 encapsulated figure

1000 Genomes-based meta-analysis identifies 10 novel loci for kidney function.

HapMap imputed genome-wide association studies (GWAS) have revealed >50 loci at which common variants with minor allele frequency >5% are associated with kidney function. GWAS using more complete reference sets for imputation, such as those from The 1000 Genomes project, promise to identify novel loci that have been missed by previous efforts. To investigate the value of such a more complete variant catalog, we conducted a GWAS meta-analysis of kidney function based on the estimated glomerular filtration rate (eGFR) in 110,517 European ancestry participants using 1000 Genomes imputed data. We identified 10 novel loci with p-value < 5 × 10(-8) previously missed by HapMap-based GWAS. Six of these loci (HOXD8, ARL15, PIK3R1, EYA4, ASTN2, and EPB41L3) are tagged by common SNPs unique to the 1000 Genomes reference panel. Using pathway analysis, we identified 39 significant (FDR < 0.05) genes and 127 significantly (FDR < 0.05) enriched gene sets, which were missed by our previous analyses. Among those, the 10 identified novel genes are part of pathways of kidney development, carbohydrate metabolism, cardiac septum development and glucose metabolism. These results highlight the utility of re-imputing from denser reference panels, until whole-genome sequencing becomes feasible in large samples