Spectra of massive QCD dirac operators from random matrix theory: All three chiral symmetry breaking patterns

The microscopic spectral eigenvalue correlations of QCD Dirac operators in the presence of dynamical fermions are calculated within the framework of Random Matrix Theory (RMT). Our approach treats the low-energy correlation functions of all three chiral symmetry breaking patterns (labeled by the Dyson index β = 1, 2 and 4) on the same footing, offering a unifying description of massive QCD Dirac spectra. RMT universality is explicitly proven for all three symmetry classes and the results are compared to the available lattice data for β = 4

Universal and non-universal behavior in Dirac spectra

We have computed ensembles of complete spectra of the staggered Dirac operator using four-dimensional SU(2) gauge fields, both in the quenched approximation and with dynamical fermions. To identify universal features in the Dirac spectrum, we compare the lattice data with predictions from chiral random matrix theory for the distribution of the low-lying eigenvalues. Good agreement is found up to some limiting energy, the so-called Thouless energy, above which random matrix theory no longer applies. We determine the dependence of the Thouless energy on the simulation parameters using the scalar susceptibility and the number variance.Comment: LATTICE98(confine), 9 pages, 11 figure

Serum albumin and mortality risk in a hyperendemic area of HCV infection in Japan

<p>Abstract</p> <p>Background</p> <p>Hypoalbuminemia has been shown to be associated with increased mortality. We reported a mass screening in 1990 of X town in Japan, which demonstrated a high prevalence of hepatitis C virus (HCV) infection. This follow-up study determined, through a period of 12 years, whether serum albumin levels impact on the life prognosis of the residents of X town.</p> <p>Results</p> <p>Of the 509 subjects, 69 had died and 55 had moved to other regions by 2002. Therefore, we analyzed 454 people for whom we could confirm life and death between 1990 and 2002. Albumin levels were assigned to two groups, low (<4.0 g/L, group A) and normal (≥4.0 g/L, group B). Of the 454 subjects analyzed, 25 were in group A and 429 in group B and the mortality was 68.0% (17/25 cases, P < 0.00001 vs. group B) and 12.1% (52/429), respectively. Mortality from hepatocellular carcinoma (HCC) was 66.7% in group A (6/9 cases, P = 0.01 vs. group B) and 15.8% (3/19) in group B. According to multivariate analysis, five factors - 50 years or older, low albumin level (<4.0 g/L), abnormal AST level, history of smoking, and absence of alcohol consumption - were associated with death. The adjusted odds ratios for these five factors were 20.65, 10.79, 2.58, 2.24 and 2.08, respectively, and each was statistically significant.</p> <p>Conclusions</p> <p>We show that the serum albumin level is an independent risk factor for mortality from all causes in the residents of X town and an important prognostic indicator. Improvement of hypoalbuminaemia should be considered for improvement of prognosis.</p

The supersymmetric technique for random-matrix ensembles with zero eigenvalues

The supersymmetric technique is applied to computing the average spectral density near zero energy in the large-N limit of the random-matrix ensembles with zero eigenvalues: B, DIII-odd, and the chiral ensembles (classes AIII, BDI, and CII). The supersymmetric calculations reproduce the existing results obtained by other methods. The effect of zero eigenvalues may be interpreted as reducing the symmetry of the zero-energy supersymmetric action by breaking a certain abelian symmetry.Comment: 22 pages, introduction modified, one reference adde

Microscopic universality with dynamical fermions

It has recently been demonstrated in quenched lattice simulations that the distribution of the low-lying eigenvalues of the QCD Dirac operator is universal and described by random-matrix theory. We present first evidence that this universality continues to hold in the presence of dynamical quarks. Data from a lattice simulation with gauge group SU(2) and dynamical staggered fermions are compared to the predictions of the chiral symplectic ensemble of random-matrix theory with massive dynamical quarks. Good agreement is found in this exploratory study. We also discuss implications of our results.Comment: 5 pages, 3 figures, minor modifications, to appear in Phys. Rev. D (Rapid Commun.

Random matrix theory and symmetric spaces

In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing the ensembles are in strict correspondence with symmetric spaces and the intrinsic characteristics of their restricted root lattices. Several important results can be obtained from this identification. In particular the Cartan classification of triplets of symmetric spaces with positive, zero and negative curvature gives rise to a new classification of random matrix ensembles. The review is organized into two main parts. In Part I the theory of symmetric spaces is reviewed with particular emphasis on the ideas relevant for appreciating the correspondence with random matrix theories. In Part II we discuss various applications of symmetric spaces to random matrix theories and in particular the new classification of disordered systems derived from the classification of symmetric spaces. We also review how the mapping from integrable Calogero--Sutherland models to symmetric spaces can be used in the theory of random matrices, with particular consequences for quantum transport problems. We conclude indicating some interesting new directions of research based on these identifications.Comment: 161 pages, LaTeX, no figures. Revised version with major additions in the second part of the review. Version accepted for publication on Physics Report

Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra

Random Matrix Theory (RMT) is a powerful statistical tool to model spectral fluctuations. This approach has also found fruitful application in Quantum Chromodynamics (QCD). Importantly, RMT provides very efficient means to separate different scales in the spectral fluctuations. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator for staggered fermions from SU(2) lattice gauge theory for different lattice size and gauge couplings. In disordered systems, the Thouless energy sets the universal scale for which RMT applies. This relates to recent theoretical studies which suggest a strong analogy between QCD and disordered systems. The wealth of data allows us to analyze several statistical measures in the bulk of the spectrum with high quality. We find deviations which allows us to give an estimate for this universal scale. Other deviations than these are seen whose possible origin is discussed. Moreover, we work out higher order correlators as well, in particular three--point correlation functions.Comment: 24 pages, 24 figures, all included except one figure, missing eps file available at http://pluto.mpi-hd.mpg.de/~wilke/diff3.eps.gz, revised version, to appear in PRD, minor modifications and corrected typos, Fig.4 revise

Low-lying Eigenvalues of the QCD Dirac Operator at Finite Temperature

We compute the low-lying spectrum of the staggered Dirac operator above and below the finite temperature phase transition in both quenched QCD and in dynamical four flavor QCD. In both cases we find, in the high temperature phase, a density with close to square root behavior, $\rho(\lambda) \sim (\lambda-\lambda_0)^{1/2}$. In the quenched simulations we find, in addition, a volume independent tail of small eigenvalues extending down to zero. In the dynamical simulations we also find a tail, decreasing with decreasing mass, at the small end of the spectrum. However, the tail falls off quite quickly and does not seem to extend to zero at these couplings. We find that the distribution of the smallest Dirac operator eigenvalues provides an efficient observable for an accurate determination of the location of the chiral phase transition, as first suggested by Jackson and Verbaarschot.Comment: LaTeX, 20 pages, 13 postscript figures. Reference added. To appear in Nucl. Phys.

Randomness on the Lattice

In this lecture we review recent lattice QCD studies of the statistical properties of the eigenvalues of the QCD Dirac operator. We find that the fluctuations of the smallest Dirac eigenvalues are described by chiral Random Matrix Theories with the global symmetries of the QCD partition function. Deviations from chiral Random Matrix Theory beyond the Thouless energy can be understood analytically by means of partially quenched chiral perturbation theory.Comment: Invited talk at the International Light-Cone Meeting on Non-Perturbative QCD and Hadron Phenomenology, Heidelberg 12-17 June 2000. 12 pages, 7 figures, Late

Gas accretion as the origin of chemical abundance gradients in distant galaxies

It has recently been suggested that galaxies in the early Universe can grow through the accretion of cold gas, and that this may have been the main driver of star formation and stellar mass growth. Because the cold gas is essentially primordial, it has a very low abundance of elements heavier than helium (metallicity). As it is funneled to the centre of a galaxy, it will lead the central gas having an overall lower metallicity than gas further from the centre, because the gas further out has been enriched by supernovae and stellar winds, and not diluted by the primordial gas. Here we report chemical abundances across three rotationally-supported star-forming galaxies at z~3, only 2 Gyr after the Big Bang. We find an 'inverse' gradient, with the central, star forming regions having a lower metallicity than less active ones, opposite to what is seen in local galaxies. We conclude that the central gas has been diluted by the accretion of primordial gas, as predicted by 'cold flow' models.Comment: To Appear in Nature Oct 14, 2010; Supplementary Information included her