Rainer Pullirsch

NON-HERMITIAN RANDOM MATRIX THEORY AND LATTICE QCD WITH CHEMICAL POTENTIAL

In quantum chromodynamics (QCD) at nonzero chemical potential, the eigenvalues of the Dirac operator are scattered in the complex plane. Can the fluctuation properties of the Dirac spectrum be described by universal predictions of non-Hermitian random matrix theory? We introduce an unfolding procedure for complex eigenvalues and apply it to data from lattice QCD at finite chemical potential

Topological lumps and dirac zero modes in Su(3) lattice gauge theory on the torus

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Evidence for quantum chaos in the plasma phase of QCD

to construct the nearest-neighbor spacing distribution of adjacent eigenvalues in the complex plane. For intermediate values of

Exact zero modes of the compact QED Dirac operator

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Spectrum of the U(1) staggered Dirac operator in four dimensions

, we find agreement with predictions of the Ginibre ensemble of random matrix theory, both in the confinement and in the deconfinement phase.

Searching for KvBLL calorons in SU(3) lattice gauge field ensembles

We compute eigenmodes of the lattice Dirac operator for quenched SU(3) gauge configurations on the 4-torus with topological charge 1. We find a strong dependence of the zero modes on the boundary conditions which we impose for the Dirac operator. The lumps seen by the eigenmodes often change their position when changing the boundary conditions, while the local chirality of the lumps remains the same. Our results show that the zero mode of a charge 1 configuration can couple to more than one object. We address the question whether these objects could be fractionally charged lumps.

Quantum chaos in compact lattice QED

Abstract We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD on a 6 3 ×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.

Density profiles of small Dirac operator eigenvalues for two color QCD at nonzero chemical potential compared to matrix models

Abstract We calculate the low-lying eigenmodes of the Neuberger overlap-Dirac operator for 4d compact lattice QED in the quenched approximation. In the strong coupling phase we find exact zero-modes, quite similar as in non-Abelian lattice QCD. Subsequently we make an attempt to identify responsible topological excitations of the U(1) lattice gauge theory.

Quantum Chaos in Supersymmetric QCD at Finite Density

We compare the low-lying spectrum of the staggered Dirac operator in the confining phase of compact U(1) gauge theory on the lattice to predictions of chiral random matrix theory. The small eigenvalues contribute to the chiral condensate similarly to the SU(2) and SU(3) gauge groups. Agreement with the chiral unitary ensemble is observed below the Thouless energy, which is extracted from the data and found to scale with the lattice size according to theoretical predictions.

Lowest eigenvalues of the Dirac operator for two color QCD at nonzero chemical potential

Abstract We discuss Kraan - van Baal - Lee - Lu (KvBLL) solutions of the classical Yang-Mills equations with temperature in the context of SU(3) lattice gauge theory. We present discretized lattice versions of KvBLL solutions and other dyonic structures, obtained by cooling in order to understand their variety and signature. An analysis of the zero modes of the lattice Dirac operator for different fermionic boundary conditions gives clear evidence for a KvBLL-like background of finite T lattice subensembles with Q = ±1 Using APE-smearing we are able to study the topological charge density q(x) of the configurations and to corroborate this interpretation.