Universal and non-universal behavior in Dirac spectra

Universal Fluctuations in Dirac Spectra

It is generally accepted that QCD with two massless quarks undergoes a chiral phase transition (see reviews by DeTar, Ukawa and Smilga for recent results on this topic). This leads to important observable signatures in the real world with two light quarks. The order parameter of the chiral phase transition is the chiral condensate 〈ψ̄ψ〉. Below the critical temperature chiral symmetry is spontane...

Universal Fluctuations in Spectra of the Lattice Dirac Operator.

Recently, Kalkreuter obtained the complete Dirac spectrum for an SU(2) lattice gauge theory. We performed a statistical analysis of his data and found that the eigenvalue correlations can be described by the Gaussian Symplectic Ensemble. Long range fluctuations are strongly suppressed: the variance of a sequence of levels containing n eigenvalues on average is given by 1 2π 2 (log n+const.). Ou...

ar X iv : h ep - l at / 9 80 90 58 v 1 1 0 Se p 19 98 1 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 t...

Universal behavior of dispersive Dirac cone in plasmonic metamaterials

Matthias Maier, ∗ Marios Mattheakis, † Efthimios Kaxiras, 3 Mitchell Luskin, and Dionisios Margetis School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA Department of Mathematics, and Insti...

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