Spectral Statistics of the Two-Body Random Ensemble Revisited

Using longer spectra we re-analyze spectral properties of the two-body random ensemble studied thirty years ago. At the center of the spectra the old results are largely confirmed, and we show that the non-ergodicity is essentially due to the variance of the lowest moments of the spectra. The longer spectra allow to test and reach the limits of validity of French's correction for the number variance. At the edge of the spectra we discuss the problems of unfolding in more detail. With a Gaussian unfolding of each spectrum the nearest neighbour spacing distribution between ground state and first exited state is shown to be stable. Using such an unfolding the distribution tends toward a semi-Poisson distribution for longer spectra. For comparison with the nuclear table ensemble we could use such unfolding obtaining similar results as in the early papers, but an ensemble with realistic splitting gives reasonable results if we just normalize the spacings in accordance with the procedure used for the data.Comment: 11 pages, 7 figure

A realistic example of chaotic tunneling: The hydrogen atom in parallel static electric and magnetic fields

Statistics of tunneling rates in the presence of chaotic classical dynamics is discussed on a realistic example: a hydrogen atom placed in parallel uniform static electric and magnetic fields, where tunneling is followed by ionization along the fields direction. Depending on the magnetic quantum number, one may observe either a standard Porter-Thomas distribution of tunneling rates or, for strong scarring by a periodic orbit parallel to the external fields, strong deviations from it. For the latter case, a simple model based on random matrix theory gives the correct distribution.Comment: Submitted to Phys. Rev.

Universal Correlations of Coulomb Blockade Conductance Peaks and the Rotation Scaling in Quantum Dots

We show that the parametric correlations of the conductance peak amplitudes of a chaotic or weakly disordered quantum dot in the Coulomb blockade regime become universal upon an appropriate scaling of the parameter. We compute the universal forms of this correlator for both cases of conserved and broken time reversal symmetry. For a symmetric dot the correlator is independent of the details in each lead such as the number of channels and their correlation. We derive a new scaling, which we call the rotation scaling, that can be computed directly from the dot's eigenfunction rotation rate or alternatively from the conductance peak heights, and therefore does not require knowledge of the spectrum of the dot. The relation of the rotation scaling to the level velocity scaling is discussed. The exact analytic form of the conductance peak correlator is derived at short distances. We also calculate the universal distributions of the average level width velocity for various values of the scaled parameter. The universality is illustrated in an Anderson model of a disordered dot.Comment: 35 pages, RevTex, 6 Postscript figure

A multi-ancestry genome-wide study incorporating gene-smoking interactions identifies multiple new loci for pulse pressure and mean arterial pressure

Elevated blood pressure (BP), a leading cause of global morbidity and mortality, is influenced by both genetic and lifestyle factors. Cigarette smoking is one such lifestyle factor. Across five ancestries, we performed a genome-wide gene–smoking interaction study of mean arterial pressure (MAP) and pulse pressure (PP) in 129 913 individuals in stage 1 and follow-up analysis in 480 178 additional individuals in stage 2. We report here 136 loci significantly associated with MAP and/or PP. Of these, 61 were previously published through main-effect analysis of BP traits, 37 were recently reported by us for systolic BP and/or diastolic BP through gene–smoking interaction analysis and 38 were newly identified (P < 5 × 10−8, false discovery rate < 0.05). We also identified nine new signals near known loci. Of the 136 loci, 8 showed significant interaction with smoking status. They include CSMD1 previously reported for insulin resistance and BP in the spontaneously hypertensive rats. Many of the 38 new loci show biologic plausibility for a role in BP regulation. SLC26A7 encodes a chloride/bicarbonate exchanger expressed in the renal outer medullary collecting duct. AVPR1A is widely expressed, including in vascular smooth muscle cells, kidney, myocardium and brain. FHAD1 is a long non-coding RNA overexpressed in heart failure. TMEM51 was associated with contractile function in cardiomyocytes. CASP9 plays a central role in cardiomyocyte apoptosis. Identified only in African ancestry were 30 novel loci. Our findings highlight the value of multi-ancestry investigations, particularly in studies of interaction with lifestyle factors, where genomic and lifestyle differences may contribute to novel findings