H. Markum

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

Evidence for quantum chaos in the plasma phase of QCD

\mu

Vacuum polarization of hadrons in lattice QCD

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

Exploring the π+-π+ Interaction in Lattice QCD

\mu

Quark multiplets and their interactions

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

QCD potentials with dynamical quarks at finite temperatures

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.

Exact zero modes of the compact QED Dirac operator

Abstract We investigate the QCD vacuum structure around static hadrons by calculating the correlations of Polyakov loops with the local chiral condensate ψ ψ( r ) and the color charge density ψ † ψ( r ) . We find that chiral symmetry is restored in the vicinity of static color sources as a consequence of gluon string creation and that virtual antiquarks screen static quarks in analogy to QED.

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

Abstract. An effective residual interaction for a meson-meson system is computed in lattice QCD. We describe the theoretical framework and present its application to the I = 2 channel S-wave interaction of the π-π system. Scattering phase shifts are also computed and compared to experimental results.

The Well defined phase of simplicial quantum gravity in four-dimensions

Abstract We investigate the potentials between static quark clusters in various SU(3)-representations below and above the deconfinement phase transition. In the confinement regime we are able to resolve in addition to the triplet-antitriplet system the triplet-sextet, the sextet-antisextet, and the octet-octet interactions at small distances. We give an explanation of the general laws for the interaction of quark clusters which have been found earlier. In the deconfinement regime we study multiplet-multiplet systems up to decuplets with high resolution. The energies at zero and infinite distance are determined by the Casimir operators.

Chiral symmetry and charge density in mesons for Kogut-Susskind and Wilson fermions

Abstract We investigate the potential between a static quark-antiquark pair in the full QCD vacuum. The dynamical quark sea is considered both by Kogut-Susskind and Wilson fermions. Two temperatures T below and above the phase transition Tc are studied. The behavior of the interquark potential in the full quantum field is driven by the explicitly broken Z3 symmetry in the fermionic action for T