Improvement of the hot QCD pressure by the minimal sensitivity criterion

The principles of minimal sensitivity (PMS) criterion is applied to the perturbative free energy density, or pressure, of hot QCD, which include the $\sim g_s^6 \ln g_s$ and part of the $\sim g_s^6$ terms. Applications are made separately to the short- and long-distance parts of the pressure. Comparison with the lattice results, at low temperatures, shows that the resultant `` optimal'' approximants are substantially improved when compared to the $\bar{MS}$ results. In particular, for the realistic case of three quark flavors, the `` optimal'' approximants are comparable with the lattice results.Comment: 14 pages, 9 figures, LaTe

Ferromagnetism of two-flavor quark matter in chiral and/or color-superconducting phases at zero and finite temperatures

We study the phase structure of the unpolarized and polarized two-flavor quark matters at zero and finite temperatures within the Nambu--Jona-Lasinio (NJL) model. We focus on the region, which includes the coexisting phase of quark-antiquark and diquark condensates. Generalizing the NJL model so as to describe the polarized quark matter, we compute the thermodynamic potential as a function of the quark chemical potential ($\mu$), the temperature ($T$), and the polarization parameter. The result heavily depends on the ratio $G_D / G_S$, where $G_S$ is the quark-antiquark coupling constant and $G_D$ is the diquark coupling constant. We find that, for small $G_D / G_S$, the "ferromagnetic" phase is energetically favored over the "paramagnetic" phase. On the other hand, for large $G_D / G_S$, there appears the window in the ($\mu, T$)-plane, in which the "paramagnetic" phase is favored.Comment: 25 pages, 10 figure

Dynamics of fine particles due to quantized vortices on the surface of superfluid 4^4He

Peculiar dynamics of a free surface of the superfluid 4He has been observed experimentally with a newly established technique utilizing a number of electrically charged fine metal particles trapped electrically at the surface by Moroshkin et al. They have reported that some portion of the particles exhibit some irregular motions and suggested the existence of quantized vortices interacting with the metal particles. We have conducted calculations with the vortex filament model, which turns out to support the idea of the vortex-particle interactions. The observed anomalous metal particle motions are roughly categorized into two types; (1) circular motions with specific frequencies, and (2) quasi-linear oscillations. The former ones seem to be explained once we consider a vertical vortex filament whose edges are terminated at the bottom and at a particle trapped at the surface. Although it is not yet clear whether all the anomalous motions are due to the quantum vortices, the vortices seem to play important roles for the motions.Comment: 7 pages, 10 figure

Dynamics of the vortex-particle complexes bound to the free surface of superfluid helium

We present an experimental and theoretical study of the 2D dynamics of electrically charged nanoparticles trapped under a free surface of superfluid helium in a static vertical electric field. We focus on the dynamics of particles driven by the interaction with quantized vortices terminating at the free surface. We identify two types of particle trajectories and the associated vortex structures: vertical linear vortices pinned at the bottom of the container and half-ring vortices travelling along the free surface of the liquid

Cancellation of energy-divergences and renormalizability in Coulomb gauge QCD within the Lagrangian formalism

In Coulomb gauge QCD in the Lagrangian formalism, energy divergences arise in individual diagrams. We give a proof on cancellation of these divergences to all orders of perturbation theory without obstructing the algebraic renormalizability of the theory.Comment: 13 pages, 7 figure

Magnetorotational Instability around a Rotating Black Hole

The magnetorotational instability(MRI) in the Kerr spacetime is studied on a 3+1 viewpoint. The Maxwell's equations are expressed in a circularly orbiting observer's frame that co-rotates with matter in Keplerian orbits. There exist large proper growth rates in MRI around a rapidly rotating black hole. The large "centrifugal force" and the rapid variations of magnetic fields are caused by the rotation of spacetime geometry. As the result, in the extreme Kerr case the maximum proper growth rate at $r=r_{ms}$ becomes about twelve times as large as that in Schwartzshield case.Comment: 18pages, 9figure

Continuous deformations of the Grover walk preserving localization

The three-state Grover walk on a line exhibits the localization effect characterized by a non-vanishing probability of the particle to stay at the origin. We present two continuous deformations of the Grover walk which preserve its localization nature. The resulting quantum walks differ in the rate at which they spread through the lattice. The velocities of the left and right-traveling probability peaks are given by the maximum of the group velocity. We find the explicit form of peak velocities in dependence on the coin parameter. Our results show that localization of the quantum walk is not a singular property of an isolated coin operator but can be found for entire families of coins