Infrared behavior of the Faddeev-Popov operator in Coulomb gauge QCD

We calculate the eigenvalue distribution of the Faddeev-Popov operator in Coulomb gauge QCD using quenched SU(3) lattice simulation. In the confinement phase, the density of the low-lying eigenvalues increases with lattice volume, and the confinement criterion is satisfied. Moreover, even in the deconfinement phase, the behavior of the FP eigenvalue density is qualitatively the same as in the confinement phase. This is consistent with the fact that the color-Coulomb potential is not screened in the deconfined phase.Comment: 10 pages, 10 figure

Leading order infrared quantum chromodynamics in Coulomb gauge

A truncation scheme for the Dyson-Schwinger equations of quantum chromodynamics in Coulomb gauge within the first order formalism is presented. The truncation is based on an Ansatz for the Coulomb kernel occurring in the action. Results at leading loop order and in the infrared are discussed for both the Yang-Mills and quark sectors. It is found that the resulting equations for the static gluon and quark propagators agree with those derived in a quasi-particle approximation to the canonical Hamiltonian approach. Moreover, a connection to the heavy quark limit is established. The equations are analyzed numerically and it is seen that in both the gluonic and quark sectors, a nontrivial dynamical infrared mass scale emerges.Comment: 27 pages, 11 figure

Scaling study of the gluon propagator in Coulomb gauge QCD on isotropic and anisotropic lattices

We calculate the transverse and time-time components of the instantaneous gluon propagator in Coulomb gauge QCD by using an SU(3) quenched lattice simulation on isotropic and anisotropic lattices. We find that the gluon propagators suffer from strong discretization effects on the isotropic lattice; on the other hand, those on the anisotropic lattices give a better scaling. Moreover, on these two type of lattices the transverse parts are significantly suppressed in the infrared region and have a turnover at about 500 [MeV]. The high resolution to the temporal direction due to the anisotropy yields small discretization errors for the time-time gluon propagators, which also show an infrared enhancement as expected in the Gribov-Zwanziger confinement scenario.Comment: 29 pages, 18 figure

Dust Size Growth and Settling in a Protoplanetary Disk

We have studied dust evolution in a quiescent or turbulent protoplanetary disk by numerically solving coagulation equation for settling dust particles, using the minimum mass solar nebular model. As a result, if we assume an ideally quiescent disk, the dust particles settle toward the disk midplane to form a gravitationally unstable layer within 2x10^3 - 4x10^4 yr at 1 - 30 AU, which is in good agreement with an analytic calculation by Nakagawa, Sekiya, & Hayashi (1986) although they did not take into account the particle size distribution explicitly. In an opposite extreme case of a globally turbulent disk, on the other hand, the dust particles fluctuate owing to turbulent motion of the gas and most particles become large enough to move inward very rapidly within 70 - 3x10^4 yr at 1 - 30 AU, depending on the strength of turbulence. Our result suggests that global turbulent motion should cease for the planetesimal formation in protoplanetary disks.Comment: 27 pages, 8 figures, accepted for publication in the Ap

Spectral sum for the color-Coulomb potential in SU(3) Coulomb gauge lattice Yang-Mills theory

We discuss the essential role of the low-lying eigenmodes of the Faddeev-Popov (FP) ghost operator on the confining color-Coulomb potential using SU(3) quenched lattice simulations in the Coulomb gauge. The color-Coulomb potential is expressed as a spectral sum of the FP ghost operator and has been explored by partially summing the FP eigenmodes. We take into account the Gribov copy effects that have a great impact on the FP eigenvalues and the color-Coulomb potential. We observe that the lowest eigenvalue vanishes in the thermodynamic limit much faster than that in the Landau gauge. The color-Coulomb potential at large distances is governed by the near-zero FP eigenmodes; in particular, the lowest one accounts for a substantial portion of the color-Coulomb string tension comparable to the Wilson string tension.Comment: 14 pages, 14 figure