Long-distance behavior of qqˉq\bar{q} color dependent potentials at finite temperature

SU(3) heavy quark potentials at finite temperature are studied with quenched lattice QCD using the stochastic gauge-fixing method. In addition to the standard color average channel, we investigate $q\bar{q}$ potentials in singlet and octet channels. % We obtain clear signals in all cases. The singlet $q\bar{q}$ channel yields an attractive force, while the octet $q\bar{q}$ potential is repulsive; the corresponding color average channel also results in an attractive force. %As the temperature increases, these forces are weakened and As the temperature increases, these forces become weak and their variations are very small; at $T/T_c=1.8-5.6$, % the singlet attractive force is not so weakened even for long distances. the singlet attractive force survives over $R \sim 1/T$. The singlet and octet potentials calculated with this algorithm have a small gauge dependence when the gauge parameter $\alpha$ is changed from 0.6 to 1.3.Comment: 12 pages, 9 figures, typos corrected, to appear in Prog. Theor. Phy

Matrix Factorizations and Representations of Quivers II: type ADE case

We study a triangulated category of graded matrix factorizations for a polynomial of type ADE. We show that it is equivalent to the derived category of finitely generated modules over the path algebra of the corresponding Dynkin quiver. Also, we discuss a special stability condition for the triangulated category in the sense of T. Bridgeland, which is naturally defined by the grading.Comment: v2: typos corrected, added an appendix by K.Ued

Incident angle dependence of reactions between graphene and hydrogen atom by molecular dynamics simulation

Incident angle dependence of reactions between graphene and hydrogen atoms are obtained qualitatively by classical molecular dynamics simulation under the NVE condition with modified Brenner reactive empirical bond order (REBO) potential. Chemical reaction depends on two parameters, i.e., polar angle $\theta$ and azimuthal angle $\phi$ of the incident hydrogen. From the simulation results, it is found that the reaction rates strongly depend on polar angle $\theta$. Reflection rate becomes larger with increasing $\theta$, and the $\theta$ dependence of adsorption rate is also found. The $\theta$ dependence is caused by three dimensional structure of the small potential barrier which covers adsorption sites. $\phi$ dependence of penetration rate is also found for large $\theta$.Comment: 4 pages, 7 figure

Nonlinear power spectrum in the presence of massive neutrinos: perturbation theory approach, galaxy bias and parameter forecasts

Future or ongoing galaxy redshift surveys can put stringent constraints on neutrinos masses via the high-precision measurements of galaxy power spectrum, when combined with cosmic microwave background (CMB) information. In this paper we develop a method to model galaxy power spectrum in the weakly nonlinear regime for a mixed dark matter (CDM plus finite-mass neutrinos) model, based on perturbation theory (PT) whose validity is well tested by simulations for a CDM model. In doing this we carefully study various aspects of the nonlinear clustering and then arrive at a useful approximation allowing for a quick computation of the nonlinear power spectrum as in the CDM case. The nonlinear galaxy bias is also included in a self-consistent manner within the PT framework. Thus the use of our PT model can give a more robust understanding of the measured galaxy power spectrum as well as allow for higher sensitivity to neutrino masses due to the gain of Fourier modes beyond the linear regime. Based on the Fisher matrix formalism, we find that BOSS or Stage-III type survey, when combined with Planck CMB information, gives a precision of total neutrino mass constraint, sigma(m_nu,tot) 0.1eV, while Stage-IV type survey may achieve sigma(m_nu,tot) 0.05eV, i.e. more than a 1-sigma detection of neutrino masses. We also discuss possible systematic errors on dark energy parameters caused by the neutrino mass uncertainty. The significant correlation between neutrino mass and dark energy parameters is found, if the information on power spectrum amplitude is included. More importantly, for Stage-IV type survey, a best-fit dark energy model may be biased and falsely away from the underlying true model by more than the 1-sigma statistical errors, if neutrino mass is ignored in the model fitting.Comment: 33 pages, 11 figure

Strange duality of weighted homogeneous polynomials

We consider a mirror symmetry between invertible weighted homogeneous polynomials in three variables. We define Dolgachev and Gabrielov numbers for them and show that we get a duality between these polynomials generalizing Arnold's strange duality between the 14 exceptional unimodal singularities.Comment: 21 pages, 1 figur