Model study of the sign problem in a mean-field approximation

We study the sign problem of the fermion determinant at nonzero baryon chemical potential. For this purpose we apply a simple model derived from Quantum Chromodynamics, in the limit of large chemical potential and mass. For SU(2) color, there is no sign problem and the mean-field approximation is similar to data from the lattice. For SU(3) color the sign problem is unavoidable, even in a mean-field approximation. We apply a phase-reweighting method, combined with the mean-field approximation, to estimate thermodynamic quantities. We also investigate the mean-field free energy using a saddle-point approximation.Comment: 7 pages, 2 figures, talk presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4, 2007, Regensburg, German

Off-diagonal kinetic theory in ultrasoft momentum region at high temperature

We derive a linearized kinetic equation for fermionic excitations with an ultrasoft momentum, g^2T, from the Kadanoff-Baym equation in a Yukawa model and quantum electrodynamics (QED) at extremely high T, where g is the coupling constant. We show that this equation is equivalent to the self-consistent equation in the resummed perturbation theory used in the analysis of the fermion spectrum with the ultrasoft momentum. Furthermore, we derive the equation that determines the n-point function with external lines for a pair of fermions and (n-2) bosons with ultrasoft momenta in QED.Comment: 15 pages, 8 figure

Charged vector mesons in a strong magnetic field

We show that charged vector mesons cannot be condensed by a magnetic field. Although some hadron models predict the charged vector meson condensation in a strong magnetic field, we prove, by means of the Vafa-Witten theorem, that this is not the case in QCD. We also perform the numerical analysis for the meson mass and condensation in lattice QCD. The lattice QCD data confirm no charged vector meson condensation in a magnetic field.Comment: 6 pages, 2 figures; some discussion improved; typos correcte

Dynamic Tax Competition under Asymmetric Productivity of Public Capital

We here expand the static tax competition models in symmetric small regions, which were indicated by Zodrow and Mieszkowski (1986) and Wilson (1986), to a dynamic tax competition model in large regions, taking consideration of the regional asymmetry of productivity of public capital and the existence of capital accumulation. The aim of this paper is to verify how the taxation policy affects asymmetric equilibrium based on a simulation analysis using an overlapping generations model in two regions. It is assumed that the public capital as a public input is formed on the basis of the capital tax of local governments and the lump-sum tax of the central government. As demonstrated in related literature, the optimal capital tax rate should become zero when the lump-sum tax is imposed only on older generations, however, the optimal tax rate may become positive when it is imposed proportionally on younger and older generations. In the asymmetric equilibrium, several cooperative solutions can possibly exist which can achieve a higher welfare standard than the actualized cooperative solution either in Region1 or 2

Magnetic Catalysis vs Magnetic Inhibition

We discuss the fate of chiral symmetry in an extremely strong magnetic field B. We investigate not only quark fluctuations but also neutral meson effects. The former would enhance the chiral-symmetry breaking at finite B according to the Magnetic Catalysis, while the latter would suppress the chiral condensate once B exceeds the scale of the hadron structure. Using a chiral model we demonstrate how neutral mesons are subject to the dimensional reduction and the low dimensionality favors the chiral-symmetric phase. We point out that this effect, the Magnetic Inhibition, can be a feasible explanation for recent lattice-QCD data indicating the decreasing behavior of the chiral-restoration temperature with increasing B.Comment: 5 pages, 2 figure

Magnetic shift of the chemical freezeout and electric charge fluctuations

We discuss the effect of a strong magnetic field on the chemical freezeout points in the ultrarelativistic heavy-ion collision. As a result of the inverse magnetic catalysis or the magnetic inhibition, the crossover onset to hot and dense matter out of quarks and gluons should be shifted to a lower temperature. To quantify this shift we employ the hadron resonance gas model and an empirical condition for the chemical freezeout. We point out that the charged particle abundances are significantly affected by the magnetic field so that the electric charge fluctuation is largely enhanced especially at high baryon density. The charge conservation partially cancels the enhancement but our calculation shows that the electric charge fluctuation and the charge chemical potential could serve as a magnetometer. We find that the fluctuation exhibits a crossover behavior rapidly increased for eB >~ (0.4GeV)^2, while the charge chemical potential has better sensitivity to the magnetic field.Comment: 5 pages, 4 figures; Fig.4 is updated for the electric charge susceptibility and the charge chemical potential as functions of

Spiral Molecular Front in Galaxies: Quick Transition from Atomic to Molecular Hydrogen in Spiral Arms

We derived a two-dimensional map of the molecular fraction, fmol, (the ratio of molecular-gas density to that of total gas) in the spiral galaxy M51, and examined the behavior of molecular fronts (MF), where MF represents the place where fmol changes drastically from nearly zero to unity and vice versa. We show that the MF phenomenon occurs not only radial, but also in the azimuth direction through the spiral arms, and fmol changes rapidly in the arm-to-inter-arm transition regions. The existence of the azimuthal MF indicates that the atomic gas (HI) is quicklytransformed to molecular gas (H_2) during the passage through spiral arms. We performed a numerical simulation of MF based on an HI-to-H_2 phase transition theory, and reproduced the observations. We estimated a azimuthal scale length of the transition to be less than 200 pc, corresponding to a time scale of about 2 Myr for H_2 gas formation. The azimuthal width of a molecular arm is estimated to be at most 2.5 kpc, where the gas can remain in molecular phase for about 25 Myr.Comment: To appear in PASJ, Latex 9 pages, 4 gif figure