A Remark on the Large Difference between the Glueball Mass and T(C) in Quenched QCD

The lattice QCD studies indicate that the critical temperature $T_c \simeq 260-280$ MeV of the deconfinement phase transition in quenched QCD is considerably smaller than the lowest-lying glueball mass $m_{\rm G} \simeq 1500-1700$ MeV, i.e., $T_c \ll m_{\rm G}$. As a consequence of this large difference, the thermal excitation of the glueball in the confinement phase is strongly suppressed by the statistical factor as $e^{-m_{\rm G}/T_c} \simeq 0.00207$ even near $T \simeq T_c$. We consider its physical implication, and argue the abnormal feature of the deconfinement phase transition in quenched QCD from the statistical viewpoint. To appreciate this, we demonstrate a statistical argument of the QCD phase transition using the recent lattice QCD data. From the phenomenological relation among $T_c$ and the glueball mass, the deconfinement transition is found to take place in quenched QCD before a reasonable amount of glueballs is thermally excited. In this way, quenched QCD reveals a question ``what is the trigger of the deconfinement phase transition ?''Comment: 6 pages, 4 figure

On the Large Time Behavior of Solutions of Hamilton-Jacobi Equations Associated with Nonlinear Boundary Conditions

In this article, we study the large time behavior of solutions of first-order Hamilton-Jacobi Equations, set in a bounded domain with nonlinear Neumann boundary conditions, including the case of dynamical boundary conditions. We establish general convergence results for viscosity solutions of these Cauchy-Neumann problems by using two fairly different methods : the first one relies only on partial differential equations methods, which provides results even when the Hamiltonians are not convex, and the second one is an optimal control/dynamical system approach, named the "weak KAM approach" which requires the convexity of Hamiltonians and gives formulas for asymptotic solutions based on Aubry-Mather sets

Time-Dependent Variational Approach to the Non-Abelian Pure Gauge Theory

The time-dependent variational approach to the pure Yang-Mills gauge theory, especially a color su(3) gauge theory, is formulated in the functional Schroedinger picture with a Gaussian wave functional approximation. The equations of motion for the quantum gauge fields are formulated in the Liouville-von Neumann form. This variational approach is applied in order to derive the transport coefficients, such as the shear viscosity, for the pure gluonic matter by using the linear response theory. As a result, the contribution to the shear viscosity from the quantum gluons is zero up to the lowest order of the coupling g in the quantum gluonic matter.Comment: 19 pages, no figures, using PTPTeX.cl

High efficiency dark-to-bright exciton conversion in carbon nanotubes

We report that dark excitons can have a large contribution to the emission intensity in carbon nanotubes due to an efficient exciton conversion from a dark state to a bright state. Time-resolved photoluminescence measurements are used to investigate decay dynamics and diffusion properties of excitons, and we obtain intrinsic lifetimes and diffusion lengths of bright excitons as well as diffusion coefficients for both bright and dark excitons. We find that the dark-to-bright transition rates can be considerably high, and that more than half of the dark excitons can be transformed into the bright excitons. The state transition rates have a large chirality dependence with a family pattern, and the conversion efficiency is found to be significantly enhanced by adsorbed air molecules on the surface of the nanotubes. Our findings show the nontrivial significance of the dark excitons on the emission kinetics in low dimensional materials, and demonstrate the potential for engineering the dark-to-bright conversion process by using surface interactions.Comment: 7 pages, 4 figure

Survival of charmonia above Tc in anisotropic lattice QCD

We find a strong evidence for the survival of $J/\Psi$ and $\eta_c$ as spatially-localized $c\bar c$ (quasi-)bound states above the QCD critical temperature $T_c$, by investigating the boundary-condition dependence of their energies and spectral functions. In a finite-volume box, there arises a boundary-condition dependence for spatially spread states, while no such dependence appears for spatially compact states. In lattice QCD, we find almost {\it no} spatial boundary-condition dependence for the energy of the $c\bar c$ system in $J/\Psi$ and $\eta_c$ channels for $T\simeq(1.11-2.07)T_c$. We also investigate the spectral function of charmonia above $T_c$ in lattice QCD using the maximum entropy method (MEM) in terms of the boundary-condition dependence. There is {\it no} spatial boundary-condition dependence for the low-lying peaks corresponding to $J/\Psi$ and $\eta_c$ around 3GeV at $1.62T_c$. These facts indicate the survival of $J/\Psi$ and $\eta_c$ as compact $c\bar c$ (quasi-)bound states for $T_c < T < 2T_c$.Comment: 4 pages, 1 figur

Nuclear Force from Lattice QCD

The first lattice QCD result on the nuclear force (the NN potential) is presented in the quenched level. The standard Wilson gauge action and the standard Wilson quark action are employed on the lattice of the size 16^3\times 24 with the gauge coupling beta=5.7 and the hopping parameter kappa=0.1665. To obtain the NN potential, we adopt a method recently proposed by CP-PACS collaboration to study the pi pi scattering phase shift. It turns out that this method provides the NN potentials which are faithful to those obtained in the analysis of NN scattering data. By identifying the equal-time Bethe-Salpeter wave function with the Schroedinger wave function for the two nucleon system, the NN potential is reconstructed so that the wave function satisfies the time-independent Schroedinger equation. In this report, we restrict ourselves to the J^P=0^+ and I=1 channel, which enables us to pick up unambiguously the ``central'' NN potential V_{central}(r). The resulting potential is seen to posses a clear repulsive core of about 500 MeV at short distance (r < 0.5 fm). Although the attraction in the intermediate and long distance regions is still missing in the present lattice set-up, our method is appeared to be quite promising in reconstructing the NN potential with lattice QCD.Comment: A talk given at the XXIV International Symposium on Lattice Field Theory (Lattice2006), Tucson, Arizona, USA, July 23-28, 2006, 3 figures, 7page

Nuclear Force from Monte Carlo Simulations of Lattice Quantum Chromodynamics

The nuclear force acting between protons and neutrons is studied in the Monte Carlo simulations of the fundamental theory of the strong interaction, the quantum chromodynamics defined on the hypercubic space-time lattice. After a brief summary of the empirical nucleon-nucleon (NN) potentials which can fit the NN scattering experiments in high precision, we outline the basic formulation to derive the potential between the extended objects such as the nucleons composed of quarks. The equal-time Bethe-Salpeter amplitude is a key ingredient for defining the NN potential on the lattice. We show the results of the numerical simulations on a $32^4$ lattice with the lattice spacing $a \simeq 0.137$fm (lattice volume (4.4 fm)$^4$) in the quenched approximation. The calculation was carried out using the massively parallel computer Blue Gene/L at KEK. We found that the calculated NN potential at low energy has basic features expected from the empirical NN potentials; attraction at long and medium distances and the repulsive core at short distance. Various future directions along this line of research are also summarized.Comment: 13 pages, 4 figures, version accepted for publication in "Computational Science & Discovery" (IOP

Anisotropic Lattice QCD Studies of Penta-quark Anti-decuplet

Anti-decuplet penta-quark baryon is studied with the quenched anisotropic lattice QCD for accurate measurement of the correlator. Both the positive and negative parity states are studied using a non-NK type interpolating field with I=0 and J=1/2. After the chiral extrapolation, the lowest positive parity state is found at m_{Theta} \simeq 2.25 GeV, which is too massive to be identified with the experimentally observed Theta^+(1540). The lowest negative parity state is found at m_{Theta}\simeq 1.75 GeV, which is rather close to the empirical value. To confirm that this state is a compact 5Q resonance, a new method with ``hybrid boundary condition (HBC)'' is proposed. The HBC analysis shows that the observed state in the negative parity channel is an NK scattering state.Comment: A talk given at International Workshop PENTAQUARK04, July 20-23, 2004 at SPring-8, Japan, 8 pages, 7 figures, 2 table