The Lattice Free Energy with Overlap Fermions: A Two-Loop Result

We calculate the 2-loop partition function of QCD on the lattice, using the Wilson formulation for gluons and the overlap-Dirac operator for fermions. Direct by-products of our result are the 2-loop free energy and average plaquette. Our calculation serves also as a prototype for further higher loop calculations in the overlap formalism. We present our results as a function of a free parameter $M_0$ entering the overlap action; the dependence on the number of colors $N$ and fermionic flavors $N_f$ is shown explicitly.Comment: 10 pages, 5 figures. Final version to appear in Physical Review D. A missing overall factor was inserted in Eq. 12; it affects also Eq. 1

Semimetalic graphene in a modulated electric potential

The $\pi$-electronic structure of graphene in the presence of a modulated electric potential is investigated by the tight-binding model. The low-energy electronic properties are strongly affected by the period and field strength. Such a field could modify the energy dispersions, destroy state degeneracy, and induce band-edge states. It should be noted that a modulated electric potential could make semiconducting graphene semimetallic, and that the onset period of such a transition relies on the field strength. There exist infinite Fermi-momentum states in sharply contrast with two crossing points (Dirac points) for graphene without external fields. The finite density of states (DOS) at the Fermi level means that there are free carriers, and, at the same time, the low DOS spectrum exhibits many prominent peaks, mainly owing to the band-edge states.Comment: 12pages, 5 figure

A simplified approach to the multi-item economic production quantity model with scrap, rework, and multi-delivery

AbstractIn a recent paper, Chiu et al. (2014) utilized mathematical modeling and differential calculus to determine the common production cycle time that minimizes total production, inventory, and delivery costs for a multi-item economic production quantity (EPQ) model with scrap, rework, and multi-delivery. The present study proposes an algebraic approach substituting the use of differential calculus on the system cost function for deriving the optimal common cycle time in the aforementioned multi-item EPQ model. This simplified approach may enable managing practitioners to resolve real multi-item EPQ models more effectively

Chiral fermions on the lattice and index relations

Comparing recent lattice results on chiral fermions and old continuum results for the index puzzling questions arise. To clarify this issue we start with a critical reconsideration of the results on finite lattices. We then work out various aspects of the continuum limit. After determining bounds and norm convergences we obtain the limit of the anomaly term. Collecting our results the index relation of the quantized theory gets established. We then compare in detail with the Atiyah-Singer theorem. Finally we analyze conventional continuum approaches.Comment: 34 pages; a more detaild introduction and a subsection with remarks on literature adde