Time-Evolution of Collective Meson Fields and Amplification of Quantum Meson Modes in Chiral Phase Transition

The time evolution of quantum meson fields in the O(4) linear sigma model is investigated in a context of the dynamical chiral phase transition. It is shown that amplitudes of quantum pion modes are amplified due to both mechanisms of a parametric resonance and a resonance by the forced oscillation according to the small oscillation of the chiral condensate in the late time of chiral phase transition.Comment: 4 pages; Talk presented at the XVIth International Conference on Particles and Nuclei (PANIC02), Sep. 30 - Oct. 4, 2002, Osaka, Japan, to appear in Nuclear Physics

Nonequilibrium chiral dynamics by the time dependent variational approach with squeezed states

We investigate the inhomogeneous chiral dynamics of the O(4) linear sigma model in 1+1 dimensions using the time dependent variational approach in the space spanned by the squeezed states. We compare two cases, with and without the Gaussian approximation for the Green's functions. We show that mode-mode correlation plays a decisive role in the out-of-equilibrium quantum dynamics of domain formation and squeezing of states.Comment: 5 pages, 4 figures. RevTex, version to appear in Phys. Rev. C. Rapid Communicatio

Scalar and Pseudoscalar Glueball Masses within a Gaussian Wavefunctional Approximation

The lowest scalar and pseudoscalar glueball masses are evaluated by means of the time-dependent variational approach to the Yang-Mills gauge theory without fermions in the Hamiltonian formalism within a Gaussian wavefunctional approximation. The glueball mass is calculated as a pole of the propagator for a composite glueball field which consists of two massless gluons. The glueball propagator is here evaluated by using the linear response theory for the composite external glueball field. As a result, a finite glueball mass is obtained through the interaction between two massless gluons, in which the glueball mass depends on the QCD coupling constant g in the nonperturbative form.Comment: 24 pages, 3 figure

Parametric Resonance versus Forced Oscillation in Time-Evolution of Quantum Meson Fields

The time-evolution of quantum meson fields in O(4)-linear sigma model is treated approximately. It is shown that the amplification of the amplitudes of pion modes with low momenta occurs by means of both the parametric resonance and the forced oscillation.Comment: 8 pages, no figure, using PTPTeX styl

Amplification of Quantum Meson Modes in the Late Time of Chiral Phase Transition

It is shown that there exists a possibility of amplification of amplitudes of quantum pion modes with low momenta in the late time of chiral phase transition by using the Gaussian wave functional approximation in the O(4) linear sigma model. It is also shown that the amplification occurs in the mechanism of the resonance by forced oscillation as well as the parametric resonance induced by the small oscillation of the chiral condensate. These mechanisms are investigated in both the case of spatially homogeneous system and the spatially expanded system described by the Bjorken coordinate.Comment: 17 pages, 16 figure

Lifetime of Collective Isospin Rotations of a Quantum Meson Field

We calculate the lifetime of the collective isospin rotating solutions which have been found recently in the case a quantum N-component meson field with exact O(N) symmetry. For this purpose we take into account the small breaking of the O(N) symmetry associated to the non vanishing mass of the pion. This term induces a coupling between collective rotations and intrinsic meson excitations. We evaluate the associated damping time in the framework of linear response theory. We find damping times of the order of 100 fm/c, i.e. substantially longer than reaction times.Comment: 20 pages, no figures, uses REVTe

Effective Potential Study of the Chiral Phase Transition in a QCD-like Theory

We construct the effective potential for a QCD-like theory using the auxiliary field method. The chiral phase transition exhibited by the model at finite temperature and the quark chemical potential is studied from the viewpoint of the shape change of the potential near the critical point. We further generalize the effective potential so as to have quark number and scalar quark densities as independent variables near the tri-critical point.Comment: 17 pages, 9 figures, using PTPTeX.cl

A Possible Extension of a Trial State in the TDHF Theory with Canonical Form in the Lipkin Model

With the aim of the extension of the TDHF theory in the canonical form in the Lipkin model, the trial state for the variation is constructed, which is an extension of the Slater determinant. The canonicity condition is imposed to formulate the variational approach in the canonical form. A possible solution of the canonicity condition is given and the zero-point fluctuation induced by the uncertainty principle is investigated. As an application, the ground state energy is evaluated.Comment: 15 pages, 1 figure, using PTPTeX styl