Gluon condensates at finite temperature

We consider various special cases of gluon condensates at finite temperature. The gluon condensate for an ideal gas of gluons with a given vacuum expectation value is introduced for the sake of comparison with that calculated using the recent finite temperature lattice gauge simulations for a pure Yang-Mills SU(3) gauge theory at the known critical temperature. We extend this comparison using the high precision lattice data for two light dynamical quarks. The investigation of these three cases show some interesting differences arising from the strong interaction alone and in the presence of quarks. In this context we discuss some newer simulations for heavier quarks and other properties related to gluon condensation.Comment: 10 pages, 2 ps-figures, Latex 2

Confining forces

We discuss the forces on the internal constituents of the hadrons based on the bag model. The ground state of the hadrons forms a color singlet so that the effects of the colored internal states are neutralized. From the breaking of the dilatation and conformal symmetries under the strong interactions the corresponding currents are not conserved. These currents give rise to the forces changing the motion of the internal particles which causes confinement.Comment: 8 pages, 2 figure

The effects of colored quark entropy on the bag pressure

We study the effects of the ground state entropy of colored quarks upon the bag pressure at low temperatures. The vacuum expectation values of the quark and gluon fields are used to express the interactions in QCD ground state in the limit of low temperatures and chemical potentials. Apparently, the inclusion of this entropy in the equation of state provides the hadron constituents with an additional heat which causes a decrease in the effective latent heat inside the hadronic bag and consequently decreases the non-perturbative bag pressure. We have considered two types of baryonic bags, $\Delta$ and $\Omega^-$. In both cases we have found that the bag pressure decreases with the temperature. On the other hand, when the colored quark ground state entropy is not considered, the bag pressure as conventionally believed remains constant for finite temperature.Comment: 13 pages, 2 eps-figures (2 parts each

Entropy for Colored Quark States at Finite Temperature

The quantum entropy at finite temperatures is analyzed by using models for colored quarks making up the physical states of the hadrons. We explicitly work out some special models for the structure of the states of SU(2) and SU(3) relating to the effects of the temperature on the quantum entropy. We show that the entropy of the singlet states monotonically decreases meaning that the mixing of these states continually diminishes with the temperature. It has been found that the structure of the octet states is more complex so that it can be best characterized by two parts. One part is very similar to that of the singlet states. The other one reflects the existence of strong correlations between two of the three color states. Furthermore, we work out the entropy for the {\it classical} Ising and the {\it quantum} XY spin chains. In Ising model the quantum (ground state) entropy does not directly enter into the canonical partition function. It also does not depend on the number of spatial dimensions, but only on the number of quantum states making up the ground state. Whereas, the XY spin chain has a finite entropy at vanishing temperature. The results from the spin models qualitatively analogous to our models for the states of SU(2) and SU(3).Comment: 19 pages, 4 eps figure

Quantum diffusion in liquid water from ring polymer molecular dynamics

We have used the ring polymer molecular-dynamics method to study the translational and orientational motions in an extended simple point charge model of liquid water under ambient conditions. We find, in agreement with previous studies, that quantum-mechanical effects increase the self-diffusion coefficient D and decrease the relaxation times around the principal axes of the water molecule by a factor of around 1.5. These results are consistent with a simple Stokes-Einstein picture of the molecular motion and suggest that the main effect of the quantum fluctuations is to decrease the viscosity of the liquid by about a third. We then go on to consider the system-size scaling of the calculated self-diffusion coefficient and show that an appropriate extrapolation to the limit of infinite system size increases D by a further factor of around 1.3 over the value obtained from a simulation of a system containing 216 water molecules. These findings are discussed in light of the widespread use of classical molecular-dynamics simulations of this sort of size to model the dynamics of aqueous systems