Progress using generalized lattice Dirac operators to parametrize the Fixed-Point QCD action

We report on an ongoing project to parametrize the Fixed-Point Dirac operator for massless quarks, using a very general construction which has arbitrarily many fermion offsets and gauge paths, the complete Clifford algebra and satisfies all required symmetries. Optimizing a specific construction with hypercubic fermion offsets, we present some preliminary results.Comment: Lattice 2000 (Improvement), 9 pages, based on a talk by K.H. and a poster by T.J. References adde

The construction of generalized Dirac operators on the lattice

We discuss the steps to construct Dirac operators which have arbitrary fermion offsets, gauge paths, a general structure in Dirac space and satisfy the basic symmetries (gauge symmetry, hermiticity condition, charge conjugation, hypercubic rotations and reflections) on the lattice. We give an extensive set of examples and offer help to add further structures.Comment: 19 pages, latex, maple code attache

Self-calibrating highly sensitive dynamic capacitance sensor: Towards rapid sensing and counting of particles in laminar flow systems

In this report we propose a sensor architecture and a corresponding read-out technique on silicon for the detection of dynamic capacitance change. This approach can be applied to rapid particle counting and single particle sensing in a fluidic system. The sensing principle is based on capacitance variation of an interdigitated electrode (IDE) structure embedded in an oscillator circuit. The capacitance scaling of the IDE results in frequency modulation of the oscillator. A demodulator architecture is employed to provide a read-out of the frequency modulation caused by the capacitance change. A self-calibrating technique is employed at the read-out amplifier stage. The capacitance variation of the IDE due to particle flow causing frequency modulation and the corresponding demodulator read-out has been analytically modelled. Experimental verification of the established model and the functionality of the sensor chip were shown using a modulating capacitor independent of fluidic integration. The initial results show that the sensor is capable of detecting frequency changes of the order of 100 parts per million (PPM), which translates to a shift of 1.43 MHz at 14.3 GHz operating frequency. It is also shown that a capacitance change every 3 μs can be accurately detected

Twisted mass fermions: neutral pion masses from disconnected contributions

Twisted mass fermions allow light quarks to be explored but with the consequence that there are mass splittings, such as between the neutral and charged pion. Using a direct calculation of the connected neutral pion correlator and stochastic methods to evaluate the disconnected correlations, we determine the neutral pion mass. We explore the dependence on lattice spacing and quark mass in quenched QCD. For dynamical QCD, we determine the sign of the splitting which is linked, via chiral PT, to the nature of the phase transition at small quark mass.Comment: 6 pages, poster (hadron spectrum and quark masses) at Lattice 2005,Dublin, July 25-3

First Physics Results at the Physical Pion Mass from Nf=2N_f = 2 Wilson Twisted Mass Fermions at Maximal Twist

We present physics results from simulations of QCD using $N_f = 2$ dynamical Wilson twisted mass fermions at the physical value of the pion mass. These simulations were enabled by the addition of the clover term to the twisted mass quark action. We show evidence that compared to previous simulations without this term, the pion mass splitting due to isospin breaking is almost completely eliminated. Using this new action, we compute the masses and decay constants of pseudoscalar mesons involving the dynamical up and down as well as valence strange and charm quarks at one value of the lattice spacing, $a \approx 0.09$ fm. Further, we determine renormalized quark masses as well as their scale-independent ratios, in excellent agreement with other lattice determinations in the continuum limit. In the baryon sector, we show that the nucleon mass is compatible with its physical value and that the masses of the $\Delta$ baryons do not show any sign of isospin breaking. Finally, we compute the electron, muon and tau lepton anomalous magnetic moments and show the results to be consistent with extrapolations of older ETMC data to the continuum and physical pion mass limits. We mostly find remarkably good agreement with phenomenology, even though we cannot take the continuum and thermodynamic limits.Comment: 45 pages, 15 figure

A first look at maximally twisted mass lattice QCD calculations at the physical point

In this contribution, a first look at simulations using maximally twisted mass Wilson fermions at the physical point is presented. A lattice action including clover and twisted mass terms is presented and the Monte Carlo histories of one run with two mass-degenerate flavours at a single lattice spacing are shown. Measurements from the light and heavy-light pseudoscalar sectors are compared to previous $N_f = 2$ results and their phenomenological values. Finally, the strategy for extending simulations to $N_f = 2 + 1 + 1$ is outlined.Comment: presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Area minimizing discs in metric spaces

We solve the classical problem of Plateau in the setting of proper metric spaces. Precisely, we prove that among all disc-type surfaces with prescribed Jordan boundary in a proper metric space there exists an area minimizing disc which moreover has a quasi-conformal parametrization. If the space supports a local quadratic isoperimetric inequality for curves we prove that such a solution is locally Hölder continuous in the interior and continuous up to the boundary. Our results generalize corresponding results of Douglas Radò and Morrey from the setting of Euclidean space and Riemannian manifolds to that of proper metric spaces

Disorder Effects in Two-Dimensional d-wave Superconductors

Influence of weak nonmagnetic impurities on the single-particle density of states $\rho(\omega)$ of two-dimensional electron systems with a conical spectrum is studied. We use a nonperturbative approach, based on replica trick with subsequent mapping of the effective action onto a one-dimensional model of interacting fermions, the latter being treated by Abelian and non-Abelian bosonization methods. It is shown that, in a d-wave superconductor, the density of states, averaged over randomness, follows a nontrivial power-law behavior near the Fermi energy: $\rho(\omega) \sim |\omega|^{\alpha}$. The exponent $\alpha>0$ is calculated for several types of disorder. We demonstrate that the property $\rho(0) = 0$ is a direct consequence of a {\it continuous} symmetry of the effective fermionic model, whose breakdown is forbidden in two dimensions. As a counter example, we consider another model with a conical spectrum - a two-dimensional orbital antiferromagnet, where static disorder leads to a finite $\rho(0)$ due to breakdown of a {\it discrete} (particle-hole) symmetry.Comment: 24 pages, 3 figures upon request, RevTe