Christian Hagen

Dual quark condensate and dressed Polyakov loops

We construct a new order parameter for finite temperature QCD by considering the quark condensate for U(1)-valued temporal boundary conditions for the fermions. Fourier transformation with respect to the boundary condition defines the dual condensate. This quantity corresponds to an equivalence class of Polyakov loops, thereby being an order parameter for the center symmetry. We explore the duality relation between the quark condensate and these dressed Polyakov loops numerically, using quenched lattice QCD configurations below and above the QCD phase transition. It is demonstrated that the Dirac spectrum responds differently to changing the boundary condition, in a manner that reproduces the expected Polyakov loop pattern. We find the dressed Polyakov loops to be dominated by the lowest Dirac modes, in contrast to thin Polyakov loops investigated earlier.

Hadron spectroscopy with dynamical chirally improved fermions

We simulate two dynamical, mass-degenerate light quarks on

Excited hadrons on the lattice : Baryons

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Complete spectra of the Dirac operator and their relation to confinement

lattices with a spatial extent of 2.4 fm using the chirally improved Dirac operator. The simulation method, the implementation of the action, and signals of equilibration are discussed in detail. Based on the eigenvalues of the Dirac operator we discuss some qualitative features of our approach. Results for ground-state masses of pseudoscalar and vector mesons as well as for the nucleon and delta baryons are presented.

Fermionic Boundary Conditions and the Finite Temperature Transition of QCD

We present results for masses of excited baryons from a quenched calculation with Chirally Improved quarks at pion masses down to 350 MeV. Our analysis of the correlators is based on the variational method. In order to provide a large basis set for spanning the physical states, we use interpolators with different Dirac structures and Jacobi smeared quark sources of different width. Our spectroscopy results for a wide range of ground state and excited baryons are discussed.

Variational method for lattice spectroscopy with ghosts

Abstract We compute complete spectra of the staggered lattice Dirac operator for quenched SU ( 3 ) gauge configurations below and above the critical temperature. The confined and the deconfined phases are characterized by a different response of the Dirac eigenvalues to a change of the fermionic boundary conditions. We analyze the role of the eigenvalues in recently developed spectral sums representing the Polyakov loop. We show that the Polyakov loop gets its main contributions from the UV end of the spectrum.

Domain decomposition improvement of quark propagator estimation

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.

Thin and dressed Polyakov loops from spectral sums of lattice differential operators

We discuss the variational method used in lattice spectroscopy calculations. In particular we address the role of ghost contributions which appear in quenched or partially quenched simulations and have a nonstandard euclidean time dependence. We show that the ghosts can be separated from the physical states. Our result is illustrated with numerical data for the scalar meson.

Ensemble averaging of conductance fluctuations in multiwall carbon nanotubes

Applying domain decomposition to the lattice Dirac operator and the associated quark propagator, we arrive at expressions which, with the proper insertion of random sources therein, can provide improvement to the estimation of the propagator. Schemes are presented for both open and closed (or loop) propagators. In the end, our technique for improving open contributions is similar to the “maximal variance reduction” approach of Michael and Peisa, but contains the advantage, especially for improved actions, of dealing directly with the Dirac operator. Using these improved open propagators for the Chirally Improved operator, we present preliminary results for the static-light meson spectrum. The improvement of closed propagators is modest: on some configurations there are signs of significant noise reduction of disconnected correlators; on others, the improvement amounts to a smoothening of the same correlators.

Masses of excited baryons from chirally improved quenched lattice QCD

We represent thin and dressed Polyakov loops as spectral sums of eigenvalues of differential operators on the lattice. For that purpose we calculate complete sets of eigenvalues of the staggered Dirac and the covariant Laplace operator for several temporal boundary conditions. The spectra from different boundary conditions can be combined such that they represent single (thin) Polyakov loops, or a collection of loops (dressed Polyakov loops). We analyze the role of the eigenvalues in the spectral sums below and above the critical temperature.