Azusa Yamaguchi

Grid: A next generation data parallel C++ QCD library

In this proceedings we discuss the motivation, implementation details, and performance of a new physics code base called Grid. It is intended to be more performant, more general, but similar in spirit to QDP++\cite{QDP}. Our approach is to engineer the basic type system to be consistently fast, rather than bolt on a few optimised routines, and we are attempt to write all our optimised routines directly in the Grid framework. It is hoped this will deliver best known practice performance across the next generation of supercomputers, which will provide programming challenges to traditional scalar codes. We illustrate the programming patterns used to implement our goals, and advances in productivity that have been enabled by using new features in C++11.

Genetic Algorithm for SU(N) gauge theory on a lattice

Abstract A hybrid algorithm is proposed for pure SU(N) lattice gauge theory based on Genetic Algorithms (GA)s and the Metropolis method. We apply the hybrid GA to pure SU(2) gauge theory on a 2-dimensional lattice and find the action per plaquette and Wilson loops being consistent with those given by the Metropolis and Heatbath methods. The thermalization of this newly proposed Hybrid GA is quite faster than in the Metropolis algorithm.An algorithm is proposed for the simulation of pure SU(N) lattice gauge theories based on Genetic Algorithms(GAs). We apply GAs to SU(2) pure gauge theory on a 2 dimensional lattice and show the results, the action per plaquette and Wilson loops, are consistent with those by Metropolis method(MP)s and Heatbath method(HB)s. Thermalization speed of GAs is especially faster than the simple MPs.

Landau gauge fixing supported by genetic algorithm

Abstract A class of algorithms for the Landau gauge fixing is proposed, which makes the steepest ascent (SA) method be more efficient by concepts of genetic algorithm. Main concern is how to incorporate random gauge transformation (RGT) to gain higher achievement of the minimal Landau gauge fixing, and to keep lower time consumption. One of these algorithms uses the block RGT, and another uses RGT controlled by local fitness density, and the last uses RGT determined by Ising Monte Carlo process. We tested these algorithms on SU(2) lattice gauge theory in 4 dimension with small βs, 2.0, 1.75 and 1.5, and report improvements in hit rate and/or in time consumption, compared to other methods.

Numerical studies of confinement in the lattice Landau gauge

Critical conjectures on confinement in the Landau gauge is numerically tested in focus to Gribov copy effects. One of the subjects is of the Kugo-Ojima confinement criterion and the other is of various viewpoints in the Gribov-Zwanziger theory. We use the smearing gauge as a reference gauge free of Gribov copy, and performed three types of simulations, log U, U-linear and log U in the smearing gauge. It is found that Gribov copy effect on the Kugo-Ojima parameter is small. log U and U-linear simulations yield only global scale factor difference in gluon propagator, but nontrivial difference of momentum behaviour in ghost propagator, and about 10% difference in Kugo-Ojima parameter. The horizon function defined by Zwanziger is evaluated in three types of gauge field and compared. All data show the negative horizon function as expected.

Genetic algorithm for lattice gauge theory. On SU(2) and U(1) on 4 dimensional lattice, how to hitchhike to thermal equilibrium state

Abstract Applying Genetic Algorithm for the Lattice Gauge Theory is formed to be an effective method to minimize the action of gauge field on a lattice. In 4 dimensions, the critical point and the Wilson loop behaviour of SU(2) lattice gauge theory as well as the phase transition of U(1) theory have been studied. The proper coding methodi has been developed in order to avoid the increase of necessary memory and the overload of calculation for Genetic Algorithm. How hichhikers toward equilibrium appear against kidnappers is clarified.

Chiral condensate and spectral flows on 2+1 flavours Domain Wall QCD from QCDOC

We present measurements of the chiral condensate and topological charge history for 2+1 flavour Domain Wall QCD, and compute spectral flows for the corresponding Hermitian Wilson Dirac operator. We considered several lattice spacings, with the DBW2 and Iwasaki gauge actions and different sea quark masses on a volume of 16 3×32 and a fifth dimension of size 8. These results show the spectral structure on 2+1 flavours of DWF QCD. We also discuss the dependence of the tunneling rate on lattice spacing and gauge action. All data was generated on the QCDOC machines.

Baryogenesis with vector-like quark model in charge transport mechanism

Abstract The electroweak barygenesis is studied in the charge transport mechanism with the vector-like quark model. Introducing an extra vector-like up-type quark and a singlet Higgs scalar with the mass of the order of a few hundred GeV, the baryon number generation from the bubble wall is estimated. We show that this scenario is consistent with the measurement of the present baryon to entropy ratio of our universe, if the parameters are in the right region.

ELECTROWEAK BARYOGENESIS AND THE PHASE TRANSITION DYNAMICS

The baryogenesis is reanalyzed based on the model by Cohen et al., in which the lepton number, generated by the neutrinos scattering from the bubble walls appearing in the development of the electroweak phase transition, is converted to the baryon number excess through the sphaleron transition. A formula obtained in this paper on the lepton number production rate is correct for both the thin and thick walls within the linear approximation. Investigation on the time development of the first order phase transition is simulated, including the temporal change of the wall velocity as well as the fusion effect of the bubbles. The details of such phase transition dynamics are found to affect considerably the final value of the baryon number excess.