614 research outputs found

    Random matrix ensembles with an effective extensive external charge

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    Recent theoretical studies of chaotic scattering have encounted ensembles of random matrices in which the eigenvalue probability density function contains a one-body factor with an exponent proportional to the number of eigenvalues. Two such ensembles have been encounted: an ensemble of unitary matrices specified by the so-called Poisson kernel, and the Laguerre ensemble of positive definite matrices. Here we consider various properties of these ensembles. Jack polynomial theory is used to prove a reproducing property of the Poisson kernel, and a certain unimodular mapping is used to demonstrate that the variance of a linear statistic is the same as in the Dyson circular ensemble. For the Laguerre ensemble, the scaled global density is calculated exactly for all even values of the parameter β\beta, while for β=2\beta = 2 (random matrices with unitary symmetry), the neighbourhood of the smallest eigenvalue is shown to be in the soft edge universality class.Comment: LaTeX209, 17 page

    Theory of random matrices with strong level confinement: orthogonal polynomial approach

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    Strongly non-Gaussian ensembles of large random matrices possessing unitary symmetry and logarithmic level repulsion are studied both in presence and absence of hard edge in their energy spectra. Employing a theory of polynomials orthogonal with respect to exponential weights we calculate with asymptotic accuracy the two-point kernel over all distance scale, and show that in the limit of large dimensions of random matrices the properly rescaled local eigenvalue correlations are independent of level confinement while global smoothed connected correlations depend on confinement potential only through the endpoints of spectrum. We also obtain exact expressions for density of levels, one- and two-point Green's functions, and prove that new universal local relationship exists for suitably normalized and rescaled connected two-point Green's function. Connection between structure of Szeg\"o function entering strong polynomial asymptotics and mean-field equation is traced.Comment: 12 pages (latex), to appear in Physical Review

    Punctuated Shutdown of Atlantic Meridional Overturning Circulation during Greenland Stadial 1.

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    The Greenland Stadial 1 (GS-1; ~12.9 to 11.65 kyr cal BP) was a period of North Atlantic cooling, thought to have been initiated by North America fresh water runoff that caused a sustained reduction of North Atlantic Meridional Overturning Circulation (AMOC), resulting in an antiphase temperature response between the hemispheres (the 'bipolar seesaw'). Here we exploit sub-fossil New Zealand kauri trees to report the first securely dated, decadally-resolved atmospheric radiocarbon ((14)C) record spanning GS-1. By precisely aligning Southern and Northern Hemisphere tree-ring (14)C records with marine (14)C sequences we document two relatively short periods of AMOC collapse during the stadial, at ~12,920-12,640 cal BP and 12,050-11,900 cal BP. In addition, our data show that the interhemispheric atmospheric (14)C offset was close to zero prior to GS-1, before reaching 'near-modern' values at ~12,660 cal BP, consistent with synchronous recovery of overturning in both hemispheres and increased Southern Ocean ventilation. Hence, sustained North Atlantic cooling across GS-1 was not driven by a prolonged AMOC reduction but probably due to an equatorward migration of the Polar Front, reducing the advection of southwesterly air masses to high latitudes. Our findings suggest opposing hemispheric temperature trends were driven by atmospheric teleconnections, rather than AMOC changes

    Universal parametric correlations in the transmission eigenvalue spectra of disordered conductors

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    We study the response of the transmission eigenvalue spectrum of disordered metallic conductors to an arbitrary external perturbation. For systems without time-reversal symmetry we find an exact non-perturbative solution for the two-point correlation function, which exhibits a new kind of universal behavior characteristic of disordered conductors. Systems with orthogonal and symplectic symmetries are studied in the hydrodynamic regime.Comment: 10 pages, written in plain TeX, Preprint OUTP-93-36S (University of Oxford), to appear in Phys. Rev. B (Rapid Communication

    Correlation functions of eigenvalues of multi-matrix models, and the limit of a time dependent matrix

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    We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of different matrices of the chain. Eventually, we consider the limit of the infinite chain of matrices, which can be interpreted as a time dependent one-matrix model, and give the correlation functions of eigenvalues at different times.Comment: Tex-Harvmac, 27 pages, submitted to Journ. Phys.

    First Direct Evidence of Chalcolithic Footwear from the Near Eastern Highlands

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    In 2008, a well preserved and complete shoe was recovered at the base of a Chalcolithic pit in the cave of Areni-1, Armenia. Here, we discuss the chronology of this find, its archaeological context and its relevance to the study of the evolution of footwear. Two leather samples and one grass sample from the shoe were dated at the Oxford Radiocarbon Accelerator Unit (ORAU). A third leather sample was dated at the University of California-Irvine Accelerator Mass Spectrometry Facility (UCIAMS). The R_Combine function for the three leather samples provides a date range of 3627–3377 Cal BC (95.4% confidence interval) and the calibrated range for the straw is contemporaneous (3627–3377 Cal BC). The shoe was stuffed with loose, unfastened grass (Poaceae) without clear orientation which was more than likely used to maintain the shape of the shoe and/or prepare it for storage. The shoe is 24.5 cm long (European size 37), 7.6 to 10 cm wide, and was made from a single piece of leather that wrapped around the foot. It was worn and shaped to the wearer's right foot, particularly around the heel and hallux where the highest pressure is exerted in normal gait. The Chalcolithic shoe provides solid evidence for the use of footwear among Old World populations at least since the Chalcolithic. Other 4th millennium discoveries of shoes (Italian and Swiss Alps), and sandals (Southern Israel) indicate that more than one type of footwear existed during the 4th millennium BC, and that we should expect to discover more regional variations in the manufacturing and style of shoes where preservation conditions permit

    A Brownian Motion Model of Parametric Correlations in Ballistic Cavities

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    A Brownian motion model is proposed to study parametric correlations in the transmission eigenvalues of open ballistic cavities. We find interesting universal properties when the eigenvalues are rescaled at the hard edge of the spectrum. We derive a formula for the power spectrum of the fluctuations of transport observables as a response to an external adiabatic perturbation. Our formula correctly recovers the Lorentzian-squared behaviour obtained by semiclassical approaches for the correlation function of conductance fluctuations.Comment: 19 pages, written in RevTe

    Comments on Hastings' Additivity Counterexamples

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    Hastings recently provided a proof of the existence of channels which violate the additivity conjecture for minimal output entropy. In this paper we present an expanded version of Hastings' proof. In addition to a careful elucidation of the details of the proof, we also present bounds for the minimal dimensions needed to obtain a counterexample.Comment: 38 page

    Palaeoclimate inferred from δ18O and palaeobotanical indicators in freshwater tufa of Lake Äntu Sinijärv, Estonia

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    We investigated a 3.75-m-long lacustrine sediment record from Lake Äntu Sinijärv, northern Estonia, which has a modeled basal age >12,800 cal yr BP. Our multi-proxy approach focused on the stable oxygen isotope composition (δ18O) of freshwater tufa. Our new palaeoclimate information for the Eastern Baltic region, based on high-resolution δ18O data (219 samples), is supported by pollen and plant macrofossil data. Radiocarbon dates were used to develop a core chronology and estimate sedimentation rates. Freshwater tufa precipitation started ca. 10,700 cal yr BP, ca. 2,000 years later than suggested by previous studies on the same lake. Younger Dryas cooling is documented clearly in Lake Äntu Sinijärv sediments by abrupt appearance of diagnostic pollen (Betula nana, Dryas octopetala), highest mineral matter content in sediments (up to 90 %) and low values of δ18O (less than −12 ‰). Globally recognized 9.3- and 8.2-ka cold events are weakly defined by negative shifts in δ18O values, to −11.3 and −11.7 ‰, respectively, and low concentrations of herb pollen and charcoal particles. The Holocene thermal maximum (HTM) is palaeobotanically well documented by the first appearance and establishment of nemoral thermophilous taxa and presence of water lilies requiring warm conditions. Isotope values show an increasing trend during the HTM, from −11.5 to −10.5 ‰. Relatively stable environmental conditions, represented by only a small-scale increase in δ18O (up to 1 ‰) and high pollen concentrations between 5,000 and 3,000 cal yr BP, were followed by a decrease in δ18O, reaching the most negative value (−12.7 ‰) recorded in the freshwater tufa ca. 900 cal yr BP
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