Related papers: Poisson Statistics in the High Temperature QCD Dir…
At zero temperature the lowest part of the spectrum of the QCD Dirac operator is known to consist of delocalized modes that are described by random matrix statistics. In the present paper we show that the nature of these eigenmodes changes…
We analyze the eigenvalue statistics of the staggered Dirac operator above $T_{c}$ in QCD with 2+1 flavors of dynamical quarks. We use physical quark masses in our simulations. We compare the eigenvalue statistics from several parts of the…
At low temperature the low end of the QCD Dirac spectrum is well described by chiral random matrix theory. In contrast, at high temperature there is no similar statistical description of the spectrum. We show that at high temperature the…
At low temperature the low-lying QCD Dirac spectrum obeys random matrix statistics. Recently we found that above $T_{c}$ the lowest part of the spectrum consists of localized modes that obey Poisson statistics. An interesting implication of…
We study the low eigenmodes of the overlap and staggered Dirac operator at high temperature. We show that the recently found localized quark modes obeying Poisson statistics are connected to physical gauge field objects with their size and…
It was previously found that at high temperature the lowest part of the QCD Dirac spectrum consists of localized modes obeying Poisson statistics. Higher up in the spectrum, modes become delocalized and their statistics can be described by…
We suggest that the lattice Dirac spectra in QCD at finite temperature may be understood using a gaussian unitary ensemble for Wilson fermions, and a chiral gaussian unitary ensemble for Kogut-Susskind fermions. For Kogut-Susskind fermions,…
In the epsilon-regime of QCD the main features of the spectrum of the low-lying eigenvalues of the (euclidean) Dirac operator are expected to be described by a certain universality class of random matrix models. In particular, the latter…
Using the overlap Dirac operator I show that, contrary to some expectations, even well above the critical temperature there is not necessarily a gap in the Dirac spectrum in pure SU(2) gauge theory. This happens when the Polyakov loop and…
We study the localization properties of the low-lying Dirac eigenmodes in QCD near the crossover temperature, using staggered fermions on the lattice. We find that localized low modes, absent at low temperature, appear at a temperature…
Chiral Random Matrix Theory has proven to describe the spectral properties of low temperature QCD very well. However, at temperatures above the chiral symmetry restoring transition it can not provide a global description. The level-spacing…
Finite temperature lattice QCD is probed by varying the temporal boundary conditions of the fermions. We develop the emerging physical behavior in a study of the quenched case and subsequently present first results for a fully dynamical…
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…
We study the Anderson-type localisation-delocalisation transition found previously in the QCD Dirac spectrum at high temperature. Using high statistics QCD simulations with $N_f=2+1$ flavours of staggered quarks, we discuss how the change…
We study complete eigenvalue spectra of the staggered Dirac matrix in quenched QCD on a $6^3\times 4$ lattice. In particular, we investigate the nearest-neighbor spacing distribution $P(s)$ for various values of $\beta$ both in the…
We discuss a possible mechanism leading to localisation of the low-lying Dirac eigenmodes in high-temperature lattice QCD, based on the spatial fluctuations of the local Polyakov lines in the partially ordered configurations above $T_c$.…
We investigate the eigenvalues and eigenvectors of the staggered Dirac operator in the vicinity of the chiral phase transition of quenched SU(3) lattice gauge theory. We consider both the global features of the spectrum and the local…
The Dirac operator in finite temperature QCD is equivalent to the Hamiltonian of an unconventional Anderson model, with on-site noise provided by the fluctuations of the Polyakov lines. The main features of its spectrum and eigenvectors,…
Random matrix theory is a powerful way to describe universal correlations of eigenvalues of complex systems. It also may serve as a schematic model for disorder in quantum systems. In this review, we discuss both types of applications of…
In this lecture we argue that the fluctuations of Dirac eigenvalues on the finest scale, i.e. on the scale of the average level spacing do not depend on the underlying dynamics and can be obtained from a chiral random matrix theory with the…