arXiv subjects

T. Wettig

Publications and source records attributed to T. Wettig.

50 records · Page 3Linked to original sources

arXiv1998

Small eigenvalues of the SU(3) Dirac operator on the lattice and in Random Matrix Theory

We have calculated complete spectra of the staggered Dirac operator on the lattice in quenched SU(3) gauge theory for β= 5.4 and various lattice sizes. The microscopic spectral density, the distribution of the smallest eigenvalue, and the two-point spectral correlation function are analyzed. We find the expected agreement of the lattice data with universal predictions of the chiral unitary ensemble of random matrix theory up to a certain energy scale, the Thouless energy. The deviations from the universal predictions are determined using the disconnected scalar susceptibility. We find that the Thouless energy scales with the lattice size as expected from theoretical arguments making use of the Gell-Mann--Oakes--Renner relation.

hep-lat↗

arXiv1998

Crossover to Non-universal Microscopic Spectral Fluctuations in Lattice Gauge Theory

The spectrum of the Dirac operator near zero virtuality obtained in lattice gauge simulations is known to be universally described by chiral random matrix theory. We address the question of the maximum energy for which this universality persists. For this purpose, we analyze large ensembles of complete spectra of the Euclidean Dirac operator for staggered fermions. We calculate the disconnected scalar susceptibility and the microscopic number variance for the chiral symplectic ensemble of random matrices and compare the results with lattice Dirac spectra for quenched SU(2). The crossover to a non-universal regime is clearly identified and found to scale with the square of the linear lattice size and with $f_π^2$, in agreement with theoretical expectations.

hep-ph↗

arXiv1998

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.

hep-lat↗

arXiv1998

Quantum chaos and QCD at finite chemical potential

We investigate the distribution of the spacings of adjacent eigenvalues of the lattice Dirac operator. At zero chemical potential $μ$, the nearest-neighbor spacing distribution $P(s)$ follows the Wigner surmise of random matrix theory both in the confinement and in the deconfinement phase. This is indicative of quantum chaos. At nonzero chemical potential, the eigenvalues of the Dirac operator become complex. We discuss how $P(s)$ can be defined in the complex plane. Numerical results from an SU(3) simulation with staggered fermions are compared with predictions from non-hermitian random matrix theory, and agreement with the Ginibre ensemble is found for $μ\approx 0.7$.

hep-lat↗

arXiv1998

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.

hep-lat↗

arXiv1998

Smallest Dirac Eigenvalue Distribution from Random Matrix Theory

We derive the hole probability and the distribution of the smallest eigenvalue of chiral hermitian random matrices corresponding to Dirac operators coupled to massive quarks in QCD. They are expressed in terms of the QCD partition function in the mesoscopic regime. Their universality is explicitly related to that of the microscopic massive Bessel kernel.

hep-th↗

arXiv1998

The microscopic spectrum of the QCD Dirac operator with finite quark masses

We compute the microscopic spectrum of the QCD Dirac operator in the presence of dynamical fermions in the framework of random-matrix theory for the chiral Gaussian unitary ensemble. We obtain results for the microscopic spectral correlators, the microscopic spectral density, and the distribution of the smallest eigenvalue for an arbitrary number of flavors, arbitrary quark masses, and arbitrary topological charge.

hep-th↗

arXiv1998

Evidence for quantum chaos in the plasma phase of QCD

We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD on a $6^3\times 4$ lattice. As a measure of the fluctuation properties of the eigenvalues, we study the nearest-neighbor spacing distribution $P(s)$ for various values of $β$ both in the confinement and in the deconfinement phase. In both phases except far into the deconfinement region, the lattice data agree with the Wigner surmise of random-matrix theory which is indicative of quantum chaos. We do not find signs of a transition to Poisson regularity at the deconfinement phase transition.

hep-ph↗

arXiv1997

Microscopic universality in the spectrum of the lattice Dirac operator

Large ensembles of complete spectra of the Euclidean Dirac operator for staggered fermions are calculated for SU(2) lattice gauge theory. The accumulation of eigenvalues near zero is analyzed as a signal of chiral symmetry breaking and compared with parameter-free predictions from chiral random matrix theory. Excellent agreement for the distribution of the smallest eigenvalue and the microscopic spectral density is found. This provides direct evidence for the conjecture that these quantities are universal functions.

hep-lat↗

arXiv1997

Random-matrix universality in the small-eigenvalue spectrum of the lattice Dirac operator

We analyze complete spectra of the lattice Dirac operator in SU(2) gauge theory and demonstrate that the distribution of low-lying eigenvalues is described by random matrix theory. We present possible practical applications of this random-matrix universality. In particular, reliable extrapolations of lattice gauge data to the thermodynamic limit are discussed.

hep-lat↗

arXiv1997

Quantum chaos in QCD at finite temperature

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 $β$ both in the confinement and deconfinement phase. In both phases except far into the deconfinement region, the data agree with the Wigner surmise of random matrix theory which is indicative of quantum chaos. No signs of a transition to Poisson regularity are found, and the reasons for this result are discussed.

hep-lat↗

arXiv1997

The chiral phase transition, random matrix models, and lattice data

We present two pieces of evidence in support of the conjecture that the microscopic spectral density of the Dirac operator is a universal quantity. First, we compare lattice data to predictions from random matrix theory. Second, we show that the functional form of the microscopic spectral correlations remains unchanged in random matrix models which take account of finite temperature. Furthermore, we present a random matrix model for the chiral phase transition in which all Matsubara frequencies are included.

hep-ph↗

arXiv1993

Factorial Moments in a Generalized Lattice Gas Model

We construct a simple multicomponent lattice gas model in one dimension in which each site can either be empty or occupied by at most one particle of any one of $D$ species. Particles interact with a nearest neighbor interaction which depends on the species involved. This model is capable of reproducing the relations between factorial moments observed in high--energy scattering experiments for moderate values of $D$. The factorial moments of the negative binomial distribution can be obtained exactly in the limit as $D$ becomes large, and two suitable prescriptions involving randomly drawn nearest neighbor interactions are given. These results indicate the need for considerable care in any attempt to extract information regarding possible critical phenomena from empirical factorial moments.

hep-ph↗

arXiv1993

High--Energy Multiparticle Distributions and a Generalized Lattice Gas Model

A simple lattice gas model in one dimension is constructed in which each site can be occupied by at most one particle of any one of $D$ species. Particles interact with a randomly drawn nearest neighbor interaction. This model is capable of reproducing the factorial moments observed in high--energy scattering. In the limit $D \rightarrow \infty$, the factorial moments of the negative binomial distribution are obtained naturally.

hep-ph↗