Topological charge using cooling and the gradient flow

The equivalence of cooling to the gradient flow when the cooling step $n_c$ and the continuous flow step of gradient flow $\tau$ are matched is generalized to gauge actions that include rectangular terms. By expanding the link variables up to subleading terms in perturbation theory, we relate $n_c$ and $\tau$ and show that the results for the topological charge become equivalent when rescaling $\tau \simeq n_c/({3-15 c_1})$ where $c_1$ is the Symanzik coefficient multiplying the rectangular term. We, subsequently, apply cooling and the gradient flow using the Wilson, the Symanzik tree-level improved and the Iwasaki gauge actions to configurations produced with $N_f=2+1+1$ twisted mass fermions. We compute the topological charge, its distribution and the correlators between cooling and gradient flow at three values of the lattice spacing demonstrating that the perturbative rescaling $\tau \simeq n_c/({3-15 c_1})$ leads to equivalent results.Comment: 21 pages, 10 figure

Liapunov Exponents and the Reversibility of Molecular Dynamics Algorithms

We study the phenomenon of lack of reversibility in molecular dynamics algorithms for the case of Wilson's lattice QCD. We demonstrate that the classical equations of motion that are employed in these algorithms are chaotic in nature. The leading Liapunov exponent is determined in a range of coupling parameters. We give a quantitative estimate of the consequences of the breakdown of reversibility due to round-off errors.Comment: Latex2e file, 4 figures, 19 page

Niedriglohnbeschäftigung in Ost- und Westdeutschland

In der Bundesrepublik Deutschland muss ein Niedriglohnsektor nicht erst noch geschaffen werden er existiert bereits. Unterstellt man einen nach West- (8,49 EUR) und Ostdeutschland (6,30 EUR) differenzierten gesetzlichen Mindestlohn, so hätten etwa 13% der abhängig Erwerbstätigen einen Anspruch darauf. Eine detaillierte Analyse des Niedriglohnsektors zeigt deutlich, dass sowohl persönliche als auch strukturelle Merkmale den Niedriglohnbezug beeinflussen. Neben der individuellen Merkmalsstruktur der Niedriglohnempfänger sind die rückläufige Tarifbindung sowie die abnehmende Tarifverbindlichkeit mögliche Gründe für die Entstehung bzw. Ausweitung des Niedriglohnsektors. Da auch die vorhandenen rechtlichen Instrumente zur Flankierung des Tarifsystems Niedriglöhne nur unzureichend regulieren können, stellt ein gesetzlicher Mindestlohn eine durchaus realistische Option für die BRD dar.A low pay sector is not to be created it already exists in Germany. Under the assumption of a separate minimum wage for the western (8.49 EUR) and the eastern (6.30 EUR) part of Germany, about 13% of the employees would have a legal entitlement to higher wages. A detailed analysis of the low pay sector shows that both personal and structural characteristics have an influence on low pay employment. Besides this, the declining rate of unionisation as well as the decreasing bindingness of collective wage agreements may be other possible reasons for the emergence or rather the broadening of the low pay sector. Furthermore the available legal regulations to firm up the system of collective bargaining do not longer countervail against low pay employment. In this respect a statutory minimum wage could be a necessarily option to regulate low wages in Germany

Applicability of Quasi-Monte Carlo for lattice systems

This project investigates the applicability of quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error scaling of observables for such theories. The error of an observable calculated by averaging over random observations generated from ordinary Monte Carlo simulations scales like $N^{-1/2}$, where $N$ is the number of observations. By means of quasi-Monte Carlo methods it is possible to improve this scaling for certain problems to $N^{-1}$, or even further if the problems are regular enough. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling of all investigated observables in both cases.Comment: on occasion of the 31st International Symposium on Lattice Field Theory - LATTICE 2013, July 29 - August 3, 2013, Mainz, Germany, 7 Pages, 4 figure