Quantum chromodynamics with various number of flavors

The phase structure of QCD with various number of flavors is studied for Wilson quarks. For the case of $N_F=3$ we find that the finite temperature deconfining transition is of first order in the chiral limit on an $N_t=4$ lattice. Together with our previous results that the deconfining transition in the chiral limit is continuous for $N_F=2$ and is first order for $N_F=6$, the order of the transition is found to be consistent with a prediction of universality. The case of $SU(2)$ QCD is also studied in the strong coupling limit and the phase structure is found to be quite similar to the case of $SU(3)$: There exists a critical number of flavors $N_F^*$ and for $N_F \geq N_F^*$ the confinement is broken even in the strong coupling limit for light quarks. $N_F^*=3$ corresponding to 7 for $SU(3)$.Comment: 3 pages with 5 PS figures, LaTeX (espcrc2.sty required), UTHEP-26

Scaling of the critical temperature and quark potential with a renormalization group improved SU(3) gauge action

We study the scaling property of the ratio of the critical temperature $T_c$ to the square root of the string tension $\sigma$ in the SU(3) pure gauge theory using a renormalization group improved action. We first determine the critical coupling $\beta_c$ on lattices with temporal extension $N_t=4$ and 6, and then calculate the static quark potential at the critical couplings on lattices at zero temperature. The values of $T_{c}/\sqrt{\sigma}$ in the infinite volume limit are identical within errors, while they are slightly larger than the value extrapolated to the continuum limit with the standard action. We also note that the rotational invariance of the static quark potential is remarkably restored in the both cases, and that the potential $V(R)$ in physical units scales in the whole region of $R$ investigated.Comment: 3 pages of Latex, 5 PostScript figures, Talk presented at LATTICE96(finite temperature

Phase structure of QCD for general number of flavors

We investigate and elucidate the phase structure of QCD for general number of flavors $N_F$ with Wilson quarks, varying $N_F$ from 2 up to 300. Based on numerical results combined with the result of the perturbation theory we propose the following picture: When $N_F \ge 17$, there is only a trivial fixed point and therefore the theory in the continuum limit is trivial. On the other hand, when $16 \ge N_F \ge 7$, there is a non-trivial fixed point and therefore the theory is non-trivial with anomalous dimensions, however, without quark confinement. Theories which satisfy both quark confinement and spontaneous chiral symmetry breaking in the continuum limit exist only for $N_F \le 6$. We also discuss the structure of the deconfining phase at finite temperatures for the small number of flavors such as $N_F=2$ and 3, through a systematic study of it for general number of flavors.Comment: LaTeX, 7 pages, 10 PS figures, Talk presented at LATTICE96(poster) and LATTICE96(finite temperature

Transport Coefficients of Quark Gluon Plasma for Pure Gauge Models

The transport coefficients of quark gluon plasma are calculated on a lattice 16**3X8, with the pure gauge models. Matsubara Green's functions of energy momentum tensors have very large fluctuations and about a few million MC sweeps are needed to reduce the errors reasonably small in the case of the standard action. They are much suppressed if Iwasaki's improved action is employed. Preliminary results show that the transport coefficients roughly depend on the coupling constant as a**(-3)(g) in the case of SU(2).Comment: Talk presented at LATTICE96(finite temperature), 3 pages in latex, 4 Postscript figure

Post-Oligarchic Evolution of Protoplanetary Embryos and the Stability of Planetary Systems

We investigate the orbit-crossing time (T_c) of protoplanet systems both with and without a gas-disk background. The protoplanets are initially with equal masses and separation (EMS systems) scaled by their mutual Hill's radii. In a gas-free environment, we find log (T_c/yr) = A+B \log (k_0/2.3). Through a simple analytical approach, we demonstrate that the evolution of the velocity dispersion in an EMS system follows a random walk. The stochastic nature of random-walk diffusion leads to (i) an increasing average eccentricity ~ t^1/2, where t is the time; (ii) Rayleigh-distributed eccentricities (P(e,t)=e/\sigma^2 \exp(-e^2/(2\sigma^2)) of the protoplanets; (iii) a power-law dependence of T_c on planetary separation. As evidence for the chaotic diffusion, the observed eccentricities of known extra solar planets can be approximated by a Rayleigh distribution. We evaluate the isolation masses of the embryos, which determine the probability of gas giant formation, as a function of the dust and gas surface densities.Comment: 15 pages, 13 figures (2 color ones), accepted for publication in Ap

Phase transition of color-superconductivity and cooling behavior of quark stars

We discuss the color-superconductivity and its effect on the cooling behavior of strange quark stars. The neutrino emissivity and specific heat of quark matter are calculated within the BCS theory. In the superconducting phase, the emissivity decreases and causes suppression of the cooling rate. It is shown that the phase transition leads to a sudden discontinuous suppression of the cooling rate in cooperation with the specific heat.Comment: 7 pages, 3 figure

Chiral Phase Transition in Lattice QCD with Wilson Quarks

The nature of the chiral phase transition in lattice QCD is studied for the cases of 2, 3 and 6 flavors with degenerate Wilson quarks, mainly on a lattice with the temporal direction extension $N_t=4$. We find that the chiral phase transition is continuous for the case of 2 flavors, while it is of first order for 3 and 6 flavors.Comment: uuencoded compressed tar file, LaTeX, 14 pages, 7 figure

Finite-temperature chiral transitions in QCD with the Wilson quark action

We investigate the finite-temperature phase structure and the scaling of the chiral condensate in lattice QCD with two degenerate light quarks, using a renormalization group improved gauge action and the Wilson quark action. We obtain a phase diagram which is consistent with that from the parity-flavor breaking scenario. The scaling relation for the chiral condensate assuming the critical exponents and the scaling function of the three dimensional O(4) model is remarkably satisfied for a wide range of parameters. This indicates that the chiral transition in two flavor QCD is of second order in the continuum limit.Comment: LaTeX, 3 pages, 4 EPS figures, Talk presented at LATTICE97 (finite temperature

Interannual differences in the regressions of the polar caps of Mars

Analyses of the behavior of the Martian polar caps in the recent spacecraft and ground based observations seem to reveal the existence of year to year variations on their regressions. In order to investigate the interannual differences in the regressions of the polar caps, the earlier data by Fischbacher et al., were reexamined, which were based on the measurements of the large number of high quality photographic plates and films collected from 1905 to 1965 at the Lowell Observatory. The results are reported and discussed