38 research outputs found

### 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

### Time-dependent variational approach in terms of squeezed coherent states: Implication to semi-classical approximation

A general framework for time-dependent variational approach in terms of squeezed coherent states is constructed with the aim of describing quantal systems by means of classical mechanics including higher order quantal effects with the aid of canonicity conditions developed in the time-dependent Hartree-Fock theory. The Maslov phase occurring in a semi-classical quantization rule is investigated in this framework. In the limit of a semi-classical approximation in this approach, it is definitely shown that the Maslov phase has a geometric nature analogous to the Berry phase. It is also indicated that this squeezed coherent state approach is a possible way to go beyond the usual WKB approximation

### A possibility of existence of a pseudovector-type quark-antiquark condensate in the quark matter and Nambu-Goldstone modes on that condensate in the Nambu-Jona-Lasinio model

A possibility of a pseudovector-type quark-antiquark condensed phase, which
leads to a quark spin polarized phase, in the quark matter is investigated
taking account of the vacuum effects leading to the chiral symmetry breaking by
using the Nambu-Jona-Lasinio model. Also, possible Nambu-Goldstone modes on the
pseudovector-type quark-antiquark condensate and the tensor-type
quark-antiquark condensate, which also leads to the quark spin polarized phase,
are investigated.Comment: 28 pages, 3 figure

### A possible framework of the Lipkin model obeying the su(n)-algebra in arbitrary fermion number. I --- The su(2)-algebras extended from the conventional fermion-pair and determination of the minimum weight states ---

The minimum weight states of the Lipkin model consisting of n single-particle
levels and obeying the su(n)-algebra are investigated systematically. The basic
idea is to use the su(2)-algebra which is independent of the su(n)-algebra.
This idea has been already presented by the present authors in the case of the
conventional Lipkin model consisting of two single-particle levels and obeying
the su(2)-algebra. If following this idea, the minimum weight states are
determined for any fermion number occupying appropriately n single-particle
levels. Naturally, the conventional minimum weight state is included: all
fermions occupy energetically the lowest single-particle level in the absence
of interaction. The cases n=2, 3, 4 and 5 are discussed in rather detail.Comment: 28 pages, 6 figur

### A possible framework of the Lipkin model obeying the su(n)-algebra in arbitrary fermion number. II --- Two subalgebras in the su(n)-Lipkin model and an approach to the construction of linearly independent basis ---

Standing on the results for the minimum weight states obtained in the
previous paper (I), an idea how to construct the linearly independent basis is
proposed for the su(n)-Lipkin model. This idea starts in setting up m
independent su(2)-subalgebras in the cases with n=2m and n=2m+1 (m=2,3,4,...).
The original representation is re-formed in terms of the spherical tensors for
the su(n)-generators built under the su(2)-subalgebras. Through this
re-formation, the su(m)-subalgebra can be found. For constructing the linearly
independent basis, not only the su(2)-algebras but also the su(m)-subalgebra
play a central role. Some concrete results in the cases with n=2, 3, 4 and 5
are presented.Comment: 25 pages, 1 figur

### Beyond the Schwinger boson representation of the su(2)-algebra. I -- New boson representation based on the su(1,1)-algebra and its related problems with application

With the use of two kinds of boson operators, a new boson representation of
the su(2)-algebra is proposed. The basic idea comes from the pseudo
su(1,1)-algebra recently given by the present authors. It forms a striking
contrast to the Schwinger boson representation of the su(2)-algebra which is
also based on two kinds of bosons. This representation may be suitable for
describing time-dependence of the system interacting with the external
environment in the framework of the thermo field dynamics formalism, i.e., the
phase space doubling. Further, several deformations related to the
su(2)-algebra in this boson representation are discussed. On the basis of these
deformed algebra, various types of time-evolution of a simple boson system are
investigated.Comment: 31 pages, 6 figure

### Spin polarization in high density quark matter under a strong external magnetic field

In high density quark matter under a strong external magnetic field, possible
phases are investigated by using the two-flavor Nambu-Jona-Lasinio model with
tensor-type four-point interaction between quarks, as well as the
axial-vector-type four-point interaction. In the tensor-type interaction under
the strong external magnetic field, it is shown that a quark spin polarized
phase is realized in all regions of the quark chemical potential under
consideration within the lowest Landau level approximation. In the
axial-vector-type interaction, it is also shown that the quark spin polarized
phase appears in the wide range of the quark chemical potential. In both the
interactions, the quark mass in zero and small chemical potential regions
increases which indicates that the chiral symmetry breaking is enhanced, namely
the magnetic catalysis occurs.Comment: 17 pages, 5 figure

### Landau-Peierls instability in a Fulde-Ferrell type inhomogeneous chiral condensed phase

We investigate the stability of an inhomogeneous chiral condensed phase
against low energy fluctuations about a spatially modulated order parameter.
This phase corresponds to the so-called dual chiral density wave in the context
of quark matter, where the chiral condensate is spatially modulated with a
finite wavevector in a single direction. From the symmetry viewpoint, the phase
realizes a locking of flavor and translational symmetries. Starting with a
Landau-Ginzburg-Wilson effective Lagrangian, we find that the associated
Nambu-Goldstone modes, whose dispersion relations are spatially anisotropic and
soft in the direction normal to the wavevector of the modulation, wash out the
long-range order at finite temperatures, but support algebraically decaying
long-range correlations. This implies that the phase can exhibit a
quasi-one-dimensional order as in liquid crystals.Comment: 24page

### Mean field theory for collective motion of quantum meson fields

Mean field theory for the time evolution of quantum meson fields is studied
in terms of the functional Schroedinger picture with a time-dependent Gaussian
variational wave functional. We first show that the equations of motion for the
variational wavefunctional can be rewritten in a compact form similar to the
Hartree-Bogoliubov equations in quantum many-body theory and this result is
used to recover the covariance of the theory. We then apply this method to the
O(N) model and present analytic solutions of the mean field evolution equations
for an N-component scalar field. These solutions correspond to quantum
rotations in isospin space and represent generalizations of the classical
solutions obtained earlier by Anselm and Ryskin. As compared to classical
solutions new effects arise because of the coupling between the average value
of the field and its quantum fluctuations. We show how to generalize these
solutions to the case of mean field dynamics at finite temperature. The
relevance of these solutions for the observation of a coherent collective state
or a disoriented chiral condensate in ultra-relativistic nuclear collisions is
discussed.Comment: 31 pages, 2 Postscript figures, uses ptptex.st