Phase structure of NJL model with weak renormalization group

We analyze the chiral phase structure of the Nambu--Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential $V(\sigma;t)$ is given as a partial differential equation, where $\sigma:=\bar \psi\psi$ and $t$ is a dimensionless RG scale. When the dynamical chiral symmetry breaking (D$\chi$SB) occurs at a certain scale $t_c$, $V(\sigma;t)$ has singularities originated from the phase transitions, and then one cannot follow RG flows after $t_c$. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the D$\chi$SB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.Comment: 32 pages, 12 figures; Version published in Nuclear Physics

The Central Gas Systems of Early-Type Galaxies Traced by Dust Feature: Based on the HST WFPC2 Archival Images

We investigated the central gas systems of E/S0 galaxies by making use of the WFPC2 images of the Hubble Space Telescope archive. We searched the gas systems that were traced by the dust with a new method of making color excess images in F555W - F814W (V-I). Out of 25 sample galaxies, we detected gas system in 14 galaxies. The dust was newly detected in two galaxies that were thought to contain no dust based on single band, pre-refurbishment data. The full extents of the gas systems are 0.1 to 3.5 kpc, and the masses of the gas, log M(gas) [M(solar)], are 4.2 to 7.2. The AGN activity is well correlated with existence of the gas systems. None of galaxies without the gas systems show the AGN activity. On the other hand, some galaxies with the gas systems show the AGN activity; optical AGN activities are shown in 5 out of 11 galaxies of which AGNs are optically studied, and radio activities are shown in 6 out of 14 galaxies. This shows that the AGN activity is driven with the gas system.Comment: gzipped tarred file containing 7 files: Tomita.tex (main text, needs aaspp4.sty), Tomita.tab[1,2].tex (tables, need aj_pt4.sty), Tomita.fig [1a,1b,1c,2].ps (PS figures). To be appeared in AJ, Vol.120, No.1 (July 2000

Optical Evidence of Itinerant-Localized Crossover of 4f4f Electrons in Cerium Compounds

Cerium (Ce)-based heavy-fermion materials have a characteristic double-peak structure (mid-IR peak) in the optical conductivity [$\sigma(\omega)$] spectra originating from the strong conduction ($c$)--$f$ electron hybridization. To clarify the behavior of the mid-IR peak at a low $c$-$f$ hybridization strength, we compared the $\sigma(\omega)$ spectra of the isostructural antiferromagnetic and heavy-fermion Ce compounds with the calculated unoccupied density of states and the spectra obtained from the impurity Anderson model. With decreasing $c$-$f$ hybridization intensity, the mid-IR peak shifts to the low-energy side owing to the renormalization of the unoccupied $4f$ state, but suddenly shifts to the high-energy side owing to the $f$-$f$ on-site Coulomb interaction at a slight localized side from the quantum critical point (QCP). This finding gives us information on the change in the electronic structure across QCP.Comment: 6 pages, 4 figures. To appear in JPSJ (Letters

Chebyshev's Bias against Splitting and Principal Primes in Global Fields

A reason for the emergence of Chebyshev's bias is investigated. The Deep Riemann Hypothesis (DRH) enables us to reveal that the bias is a natural phenomenon for making a well-balanced disposition of the whole sequence of primes, in the sense that the Euler product converges at the center. By means of a weighted counting function of primes, we succeed in expressing magnitudes of the deflection by a certain asymptotic formula under the assumption of DRH, which gives a new formulation of Chebyshev's bias. For any Galois extension of global fields and for any element $\sigma$ in the Galois group, we establish a criterion of the bias of primes whose Frobenius elements are equal to $\sigma$ under the assumption of DRH. As an application we obtain a bias toward non-splitting and non-principle primes in abelian extensions under DRH. In positive characteristic cases, DRH is proved, and all these results hold unconditionally

Scaling Bubble Entrainment And Dispersion In Vertical Circular Plunging Jet Flows: Freshwater Versus Seawater

At a plunging jet, air entrainment may take place downstream of the impingement perimeter. This study investigates air entrainment and bubble dispersion at vertical circular plunging jets in freshwater, salty freshwater and seawater. The results show lesser air entrainment in seawater plunging jets for identical inflow conditions. The average pseudo-chord sizes are between 4 and 6 mm for all water solutions, although more fine bubbles were detected in seawater. It is believed that surfactants and bio-chemicals harden the induction trumpet at plunge point and diminish air entrapment at impingement in seawater