Overdamping Phenomena near the Critical Point in O(NN) Model

We consider the dynamic critical behavior of the propagating mode for the order parameter fluctuation of the O($N$) Ginzburg-Landau theory, involving the canonical momentum as a degree of freedom. We reexamine the renormalization group analysis of the Langevin equation for the propagating mode. We find the fixed point for the propagating mode as well as that for the diffusive one, the former of which is unstable to the latter. This indicates that the propagating mode becomes overdamped near the critical point. We thus can have a sufficient understanding of the phonon mode in the structural phase transition of solids. We also discuss the implication for the chiral phase transition.Comment: 5 pages, 1 figure;v3 modification for correcting a misleading description, conclusion unchange

Derivation of Covariant Dissipative Fluid Dynamics in the Renormalization-group Method

We derive generic relativistic hydrodynamical equations with dissipative effects from the underlying Boltzmann equation in a mechanical and systematic way on the basis of so called the renormalization-group (RG) method. A macroscopic frame vector is introduced to specify the frame on which the macroscopic dynamics is described. Our method is so mechanical with only few ansatz that our method give a microscopic foundation of the available hydrodynamical equations, and also can be applied to make a reduction of the kinetic equations other than the simple Boltzmann equation.Comment: Serious typos and a minor one are corrected in p.6 and 7, and in p.1, respectivel

Phase diagram at finite temperature and quark density in the strong coupling region of lattice QCD for color SU(3)

We study the phase diagram of quark matter at finite temperature (T) and chemical potential (mu) in the strong coupling region of lattice QCD for color SU(3). Baryon has effects to extend the hadron phase to a larger mu direction relative to Tc at low temperatures in the strong coupling limit. With the 1/g^2 corrections, Tc is found to decrease rapidly as g decreases, and the shape of the phase diagram becomes closer to that expected in the real world.Comment: 4 pages, 4 figures. To appear in the proceedings of the 19th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions, Shanghai, China, Nov. 14-20, 2006 (Quark Matter 2006

Brown-Rho Scaling in the Strong Coupling Lattice QCD

We examine the Brown-Rho scaling for meson masses in the strong coupling limit of lattice QCD with one species of staggered fermion. Analytical expression of meson masses is derived at finite temperature and chemical potential. We find that meson masses are approximately proportional to the equilibrium value of the chiral condensate, which evolves as a function of temperature and chemical potential.Comment: Prepared for Chiral Symmetry in Hadron and Nuclear Physics (Chiral07), Nov. 13-16, 2007, Osaka, Japa

Multi-phases in gauge theories on non-simply connected spaces

It is pointed out that phase structures of gauge theories compactified on non-simply connected spaces are not trivial. As a demonstration, an SU(2) gauge model on $M^3\otimes S^1$ is studied and is shown to possess three phases: Hosotani, Higgs and coexisting phases. The critical radius and the order of the phase transitions are explicitly determined. A general discussion about phase structures for small and large scales of compactified spaces is given. The appearance of phase transitions suggests a GUT scenario in which the gauge hierarchy problem is replaced by a dynamical problem of how to stabilize a radius of a compactified space in close vicinity to a critical radius.Comment: 12 pages, 1 figur