arXiv subjects

Elmar Bittner

Publications and source records attributed to Elmar Bittner.

28 records · Page 2Linked to original sources

arXiv2004

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

We investigate the eigenvalue spectrum of the staggered Dirac matrix in two color QCD at finite chemical potential. The profiles of complex eigenvalues close to the origin are compared to a complex generalization of the chiral Gaussian Symplectic Ensemble, confirming its predictions for weak and strong non-Hermiticity. They differ from the QCD symmetry class with three colors by a level repulsion from both the real and imaginary axis.

hep-lat↗

arXiv2004

Quantum chaos in supersymmetric QCD at finite density

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 and we discuss how $P(s)$ can be defined in the complex plane. Numerical results from an SU(2) simulation with staggered fermions in fundamental and adjoint representations are compared with predictions from non-hermitian random matrix theory, and agreement with the Ginibre ensemble is found for $μ\approx 0.5$.

hep-lat↗

arXiv2002

On the Continuum Limit of the Discrete Regge Model in 4d

The Regge Calculus approximates a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The Discrete Regge model employed in this work limits the choice of the link lengths to a finite number. This makes the computational evaluation of the path integral much faster. A main concern in lattice field theories is the existence of a continuum limit which requires the existence of a continuous phase transition. The recently conjectured second-order transition of the four-dimensional Regge skeleton at negative gravity coupling could be such a candidate. We examine this regime with Monte Carlo simulations and critically discuss its behavior.

hep-lat↗

arXiv2001

Quantum Chaos in Physical Systems: from Super Conductors to Quarks

This article is the written version of a talk delivered at the Bexbach Colloquium of Science 2000 and starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is formulated and evaluated within random-matrix theory. Several examples of physical systems exhibiting quantum chaos ranging from nuclear to solid state physics are presented. The presentation concludes with recent research work on quantum chromodynamics and the quark-gluon plasma. In the case of a chemical potential the eigenvalue spectrum becomes complex and one has to deal with non-Hermitian random-matrix theory.

hep-lat↗

arXiv2001

Lowest eigenvalues of the Dirac operator for two color QCD at finite density

We investigate the eigenvalue spectrum of the staggered Dirac matrix in full QCD with two colors and finite chemical potential. Along the strong-coupling axis up to the temperature phase transition, the low-lying Dirac spectrum is well described by random matrix theory (RMT) and exhibits universal behavior. The situation is discussed in the chirally symmetric phase and no universality is seen for the microscopic spectral density.

hep-lat↗

arXiv2001

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

We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) and U(1) gauge theory as well as in full QCD with two colors and finite chemical potential. Along the strong-coupling axis up to the phase transition, the low-lying Dirac spectrum of these quantum field theories is well described by random matrix theory and exhibits universal behavior. Related results for gauge theories with minimal coupling are discussed in the chirally symmetric phase and no universality is seen for the microscopic spectral densities.

hep-lat↗

arXiv2001

Spins coupled to a $Z_2$-Regge lattice in 4d

We study an Ising spin system coupled to a fluctuating four-dimensional $Z_2$-Regge lattice and compare with the results of the four-dimensional Ising model on a regular lattice. Particular emphasis is placed on the phase transition of the spin system and the associated critical exponents. We present results from finite-size scaling analyses of extensive Monte Carlo simulations which are consistent with mean-field predictions.

hep-lat↗

arXiv2000

Dirac and Gor'kov spectra in two color QCD with chemical potential

We analyze the eigenvalue spectrum of the staggered Dirac matrix in two-color QCD at nonzero baryon density when the eigenvalues become complex. The quasi-zero modes and their role for chiral symmetry breaking and the deconfinement transition are examined. The bulk of the spectrum and its relation to quantum chaos is considered. A comparison with predictions from random matrix theory is presented. An analogous analysis is performed for the spectrum of the Gor'kov representation of the fermionic action.

hep-lat↗

arXiv2000

Eigenvalues of the QCD Dirac operator at finite temperature and density

We investigate the eigenvalue spectrum of the staggered Dirac matrix in two-color QCD at nonzero temperature and at baryon density when the eigenvalues become complex. The quasi-zero modes and their role for chiral symmetry breaking and the deconfinement transition are examined. The bulk of the spectrum and its relation to quantum chaos is considered. Comparison with predictions from random matrix theory is presented.

hep-ph↗

arXiv2000

Quantum chaos and chiral symmetry at the QCD and QED phase transition

We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD as well as in quenched U(1) theory. As a measure of the fluctuation properties of the eigenvalues, we consider the nearest-neighbor spacing distribution. We find that in all regions of their phase diagrams, compact lattice gauge theories have bulk spectral correlations given by random matrix theory, which is an indication for quantum chaos. In the confinement phase, the low-lying Dirac spectrum of these quantum field theories is well described by random matrix theory, exhibiting universal behavior. Related results for gauge theories with minimal coupling are now discussed also in the chirally symmetric phase.

hep-lat↗