Topological Phases in Neuberger-Dirac operator

The response of the Neuberger-Dirac fermion operator D=\Id + V in the topologically nontrivial background gauge field depends on the negative mass parameter $m_0$ in the Wilson-Dirac fermion operator $D_w$ which enters $D$ through the unitary operator $V = D_w (D_w^{\dagger} D_w)^{-1/2}$. We classify the topological phases of $D$ by comparing its index to the topological charge of the smooth background gauge field. An exact discrete symmetry in the topological phase diagram is proved for any gauge configurations. A formula for the index of D in each topological phase is derived by obtaining the total chiral charge of the zero modes in the exact solution of the free fermion propagator.Comment: 27 pages, Latex, 3 figures, appendix A has been revise

Sintered silicon nitrode recuperator fabrication

The preliminary design and a demonstration of the feasibility of fabricating submodules of an automotive Stirling engine recuperator for waste heat recovery at 370 C are described. Sinterable silicon nitride (Sialon) tubing and plates were fabricated by extrusion and hydrostatic pressing, respectively, suitable for demonstrating a potential method of constructing ceramic recuperator-type heat exchangers. These components were fired in nitrogen atmosphere to 1800 C without significant scale formation so that they can be used in the as-fired condition. A refractory glass composition (Al2O3 x 4.5 CaO.MgO x 11SiO2) was used to join and seal component parts by a brazing technique which formed strong recuperator submodules capable of withstanding repeated thermal cycling to 1370 C. The corrosion resistance of these materials to Na2SO4 + NaCl carbon mixtures was also assessed in atmospheres of air, hydrogen and CO2-N2-H2O mixtures at both 870 C and 1370 C for times to 1000 hours. No significant reaction was observed under any of these test conditions

A note on Zolotarev optimal rational approximation for the overlap Dirac operator

We discuss the salient features of Zolotarev optimal rational approximation for the inverse square root function, in particular, for its applications in lattice QCD with overlap Dirac quark. The theoretical error bound for the matrix-vector multiplication $H_w (H_w^2)^{-1/2}Y$ is derived. We check that the error bound is always satisfied amply, for any QCD gauge configurations we have tested. An empirical formula for the error bound is determined, together with its numerical values (by evaluating elliptic functions) listed in Table 2 as well as plotted in Figure 3. Our results suggest that with Zolotarev approximation to $(H_w^2)^{-1/2}$, one can practically preserve the exact chiral symmetry of the overlap Dirac operator to very high precision, for any gauge configurations on a finite lattice.Comment: 23 pages, 5 eps figures, v2:minor clarifications, and references added, to appear in Phys. Rev.

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

Influence of retardation effects on 2D magnetoplasmon spectrum

Within dissipationless limit the magnetic field dependence of magnetoplasmon spectrum for unbounded 2DEG system found to intersect the cyclotron resonance line, and, then approaches the frequency given by light dispersion relation. Recent experiments done for macroscopic disc-shape 2DEG systems confirm theory expectations.Comment: 2 pages,2 figure

THE STUDY OF RELATED FACTORS WITH BALL VELOCITY OF THROWING OF GIRLS AGED 11-12 YEARS OLD

INTRODUCTION: The forceful overarm throwing is considered a fundamental movement for many skills. In addition, it is also regards as a characteristic of child’s development. As to the researches of development, gender difference is also concerned by experts of development. Research related to child motor development traditionally follow the structure of Burton’s (1992) on amendment of Development Sequences for Overhand Throwing table to measure throwing patterns. But overarm throwing is a kind of fast motion especially for the period which is from backswing to release. The traditional way mentioned above can’t provide detailed data. The purpose of the study was to find out the related factors with ball velocity of throwing of girls aged 11-12 years

Quenched chiral logarithms in lattice QCD with exact chiral symmetry

We examine quenched chiral logarithms in lattice QCD with overlap Dirac quark. For 100 gauge configurations generated with the Wilson gauge action at $\beta = 5.8$ on the $8^3 \times 24$ lattice, we compute quenched quark propagators for 12 bare quark masses. The pion decay constant is extracted from the pion propagator, and from which the lattice spacing is determined to be 0.147 fm. The presence of quenched chiral logarithm in the pion mass is confirmed, and its coefficient is determined to be $\delta = 0.203 \pm 0.014$, in agreement with the theoretical estimate in quenched chiral perturbation theory. Further, we obtain the topological susceptibility of these 100 gauge configurations by measuring the index of the overlap Dirac operator. Using a formula due to exact chiral symmetry, we obtain the $\eta'$ mass in quenched chiral perturbation theory, $m_{\eta'} = (901 \pm 64)$ Mev, and an estimate of $\delta = 0.197 \pm 0.027$, which is in good agreement with that determined from the pion mass.Comment: 24 pages, 6 EPS figures; v2: some clarifications added, to appear in Physical Review

On the continuum limit of fermionic topological charge in lattice gauge theory

It is proved that the fermionic topological charge of SU(N) lattice gauge fields on the 4-torus, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of the Overlap Dirac operator, reduces to the continuum topological charge in the classical continuum limit when the parameter $m_0$ is in the physical region $0<m_0<2$.Comment: latex, 18 pages. v2: Several comments added. To appear in J.Math.Phy

Stops and MET: the shape of things to come

LHC experiments have placed strong bounds on the production of supersymmetric colored particles (squarks and gluinos), under the assumption that all flavors of squarks are nearly degenerate. However, the current experimental constraints on stop squarks are much weaker, due to the smaller production cross section and difficult backgrounds. While light stops are motivated by naturalness arguments, it has been suggested that such particles become nearly impossible to detect near the limit where their mass is degenerate with the sum of the masses of their decay products. We show that this is not the case, and that searches based on missing transverse energy (MET) have significant reach for stop masses above 175 GeV, even in the degenerate limit. We consider direct pair production of stops, decaying to invisible LSPs and tops with either hadronic or semi-leptonic final states. Modest intrinsic differences in MET are magnified by boosted kinematics and by shape analyses of MET or suitably-chosen observables related to MET. For these observables we show that the distributions of the relevant backgrounds and signals are well-described by simple analytic functions, in the kinematic regime where signal is enhanced. Shape analyses of MET-related distributions will allow the LHC experiments to place significantly improved bounds on stop squarks, even in scenarios where the stop-LSP mass difference is degenerate with the top mass. Assuming 20/fb of luminosity at 8 TeV, we conservatively estimate that experiments can exclude or discover degenerate stops with mass as large as ~ 360 GeV and 560 GeV for massless LSPs.Comment: Version submitted to journal with improved analysis and small fixes, 27 pages, 11 figures, 2 table