1,148 research outputs found

    Angular Gelfand--Tzetlin Coordinates for the Supergroup UOSp(k_1/2k_2)

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    We construct Gelfand--Tzetlin coordinates for the unitary orthosymplectic supergroup UOSp(k_1/2k_2). This extends a previous construction for the unitary supergroup U(k_1/k_2). We focus on the angular Gelfand--Tzetlin coordinates, i.e. our coordinates stay in the space of the supergroup. We also present a generalized Gelfand pattern for the supergroup UOSp(k_1/2k_2) and discuss various implications for representation theory

    Between Poisson and GUE statistics: Role of the Breit-Wigner width

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    We consider the spectral statistics of the superposition of a random diagonal matrix and a GUE matrix. By means of two alternative superanalytic approaches, the coset method and the graded eigenvalue method, we derive the two-level correlation function X2(r)X_2(r) and the number variance Σ2(r)\Sigma^2(r). The graded eigenvalue approach leads to an expression for X2(r)X_2(r) which is valid for all values of the parameter λ\lambda governing the strength of the GUE admixture on the unfolded scale. A new twofold integration representation is found which can be easily evaluated numerically. For λ1\lambda \gg 1 the Breit-Wigner width Γ1\Gamma_1 measured in units of the mean level spacing DD is much larger than unity. In this limit, closed analytical expression for X2(r)X_2(r) and Σ2(r)\Sigma^2(r) can be derived by (i) evaluating the double integral perturbatively or (ii) an ab initio perturbative calculation employing the coset method. The instructive comparison between both approaches reveals that random fluctuations of Γ1\Gamma_1 manifest themselves in modifications of the spectral statistics. The energy scale which determines the deviation of the statistical properties from GUE behavior is given by Γ1\sqrt{\Gamma_1}. This is rigorously shown and discussed in great detail. The Breit-Wigner Γ1\Gamma_1 width itself governs the approach to the Poisson limit for rr\to\infty. Our analytical findings are confirmed by numerical simulations of an ensemble of 500×500500\times 500 matrices, which demonstrate the universal validity of our results after proper unfolding.Comment: 25 pages, revtex, 5 figures, Postscript file also available at http://germania.ups-tlse.fr/frah

    Spectral correlations of the massive QCD Dirac operator at finite temperature

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    We use the graded eigenvalue method, a variant of the supersymmetry technique, to compute the universal spectral correlations of the QCD Dirac operator in the presence of massive dynamical quarks. The calculation is done for the chiral Gaussian unitary ensemble of random matrix theory with an arbitrary Hermitian matrix added to the Dirac matrix. This case is of interest for schematic models of QCD at finite temperature.Comment: 19 pages, no figures, LaTeX (elsart.cls) minor changes, one reference adde