Julia Danzer

Chiral symmetry and spectral properties of the Dirac operator in G2 Yang-Mills theory

We study spontaneous chiral symmetry breaking and the spectral properties of the staggered lattice Dirac operator using quenched gauge configurations for the exceptional group G2, which has a trivial center. In particular we study the system below and above the finite temperature transition and use the temporal boundary conditions of the fermions to probe the system. We evaluate several observables: The spectral density at the origin, the spectral gap, the chiral condensate and the recently proposed dual chiral condensate. We show that chiral symmetry is broken at low temperatures and is restored at high temperatures at the thermodynamic phase transition. Concerning the role of the boundary conditions we establish that in all respects the spectral quantities behave for G2 in exactly the same way as for SU(N), when for the latter group the gauge ensemble above Tc is restricted to the sector of configurations with real Polyakov loop.

Fermionic Boundary Conditions and the Finite Temperature Transition of QCD

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 calculation comparing ensembles below and above the phase transition. We show that for low temperature spectral quantities of the Dirac operator are insensitive to boundary conditions, while in the deconfined phase a non-trivial response to a variation of the boundary conditions sets in.

Properties of canonical determinants and a test of fugacity expansion for finite density lattice QCD with Wilson fermions

We analyze canonical determinants, i.e., grand canonical determinants projected to a fixed net quark number. The canonical determinants are the coefficients in a fugacity expansion of the grand canonical determinant and we evaluate them as the Fourier moments of the grand canonical determinant with respect to imaginary chemical potential, using a dimensional reduction technique. The analysis is done for two mass-degenerate flavors of Wilson fermions at several temperatures below and above the confinement/deconfinement crossover. We discuss various properties of the canonical determinants and analyse the convergence of the fugacity series for different temperatures.

Canonical fermion determinants in lattice QCD – Numerical evaluation and properties

Abstract We analyze canonical fermion determinants, i.e., fermion determinants projected to a fixed quark number q. The canonical determinants are computed using a dimensional reduction formula and are studied for pure SU ( 3 ) gauge configurations in a wide range of temperatures. It is demonstrated that the center sectors of the Polyakov loop very strongly manifest themselves in the behavior of the canonical determinants in the deconfined phase, and we discuss physical implications of this finding. Furthermore the distribution of the quark sectors is studied as a function of the temperature.

Coherent center domains from local Polyakov loops

We analyze properties of local Polyakov loops using quenched as well as dynamical SU(3) gauge configurations for a wide range of temperatures. It is demonstrated that for both, the confined and the deconfined regime, the local Polyakov loop prefers phase values near the center elements 1,e±i2π/3. We divide the lattice sites into three sectors according to these phases and show that the sectors give rise to the formation of clusters. For a suitable definition of these clusters we find that in the quenched case deconfinement manifests itself as the onset of percolation of the clusters. A possible continuum limit of the center clusters is discussed.

A study of the sign problem for lattice QCD with chemical potential

Abstract We study the expectation value of the phase of the fermion determinant for Wilson lattice fermions with chemical potential. We use quenched SU ( 3 ) ensembles and implement a recently proposed exact dimensional reduction of the fermion determinant. Ensembles at several temperatures below and above the phase transition are studied and we analyze the role of the quark mass, the temperature, the volume and the topological sectors. We compare our numerical results to predictions from chiral perturbation theory.

Properties of canonical fermion determinants with a fixed quark number

Using a dimensional reduction formula for the lattice fermion determinant we study canonical determinants on quenched SU(3) gauge configurations. The ca nonical determinants decribe a fixed quark number and we analyze their properties below and a bove the transition temperature. We find that above Tc the signatures of center symmetry breaking are very strongly manifest in the distribution of the canonical determinants in the complex plane, and we discuss possible physical implications of this finding. We furthermore analyze the rel ative weight of the different quark sectors below and above the transition temperature.

Comparison study of COSMIC RO dry air climatologies based on average profile inversion

Global Navigation Satellite System (GNSS) Radio Occultation (RO) data enable the retrieval of near vertical profiles of atmospheric parameters like bending angle, refractivity, pressure and temperature. The retrieval step from bending angle to refractivity, however, involves an Abel integral, whose upper limit is infinity. RO data are practically limited to altitudes below about 80 km and the observed bending angle profiles show decreasing signal-to-noise ratio with increasing altitude. Some kind 5 of high-altitude background data are therefore needed, in order to perform this retrieval step (this approach is known as “highaltitude initialization”). Any bias in the background data will affect all RO data products beyond bending angle. A reduction of the influence of the background is therefore desirable in particular for climate applications. Recently a new approach for the production of GNSS radio occultation climatologies has been proposed. The idea is to perform the averaging of individual profiles in bending angle space and then propagate the mean bending angle profiles through 10 the Abel transform. Climatological products of refractivity, density, pressure, and temperature are directly retrieved from the mean bending angles. The averaging of a large number of profiles suppresses noise in the data, enabling observed bending angle data to be used up to 80 km without the need of a priori information. Some background information for the Abel integral is still necessary above 80 km. 15 This work is a follow-up study, having the focus on the comparison of the average profile inversion climatologies (API) from the two processing centers WEGC and DMI, studying monthly COSMIC (Constellation Observing System for Meteorology, Ionosphere, and Climate) data from January to March 2011. The impact of different backgrounds above 80 km is tested, and different implementations of the Abel integral are investigated. Results are compared for the climatological products against ECMWF analyses, MIPAS, and SABER data. 20 It is shown that different implementations of the Abel integral have little impact on the API climatologies. On the other hand, different extrapolations of the bending angle profile above 80 km play a key role on the resulting monthly mean refractivities above 35 km altitude. Below that respective altitude the API climatologies show a good agreement between the two processing centers WEGC and DMI. Due to the downward propagation within the retrieval, effects of the high altitude initialization lead to differences in dry temperature climatologies down to 20 km altitude. 25