Large-N Collective Field Theory Applied to Anyons in Magnetic Fields

We present a large-$N$ collective field formalism for anyons in external magnetic fields interacting with arbitrary two-body potential. We discuss how the Landau level is reproduced in our framework. We apply it to the soluble model for anyons proposed by Girvin et al., and obtain the dispersion relation of collective modes for arbitrary statistical parameters.Comment: 10 pages(Plain TeX) TMUP-HEL-930

Parametric resonance at the critical temperature in high energy heavy ion collisions

Parametric resonance in soft modes at the critical temperature ($T_{c}$) in high energy heavy ion collisions is studied in the case when the temperature ($T$) of the system is almost constant for a long time. By deviding the fields into three parts, zero mode (condensate), soft modes and hard modes and assuming that the hard modes are in thermal equilibrium, we derive the equation of motion for soft modes at $T=T_{c}$. Enhanced modes are extracted by comparing with the Mathieu equation for the condensate oscillating along the sigma axis at $T=T_{c}$. It is found that the soft mode of $\pi$ fields at about 174 MeV is enhanced.Comment: 8 pages, 1 figure Some statements and equations are modified to clarif

Quantum description for a chiral condensate disoriented in a certain direction in isospace

We derive a quantum state of the disoriented chiral condensate dynamically, considering small quantum fluctuations around a classical chiral condensate disoriented in a certain direction $\vec n$ in isospace. The obtained nonisosinglet quantum state has the characteristic features; (i) it has the form of the squeezed state, (ii) the state contains not only the component of pion quanta in the direction $\vec n$ but also the component in the perpendicular direction to $\vec n$ and (iii) the low momentum pions in the state violate the isospin symmetry. With the quantum state, we calculate the probability of the neutral fraction depending on the time and the pion's momentum, and find that the probability has an unfamiliar form. For the low momentum pions, the parametric resonance mechanism works with the result that the probability of the neutral fraction becomes the well known form approximately and that the charge fluctuation is small.Comment: 19 page

Description of a domain by a squeezed state in a scalar field theory

The author attempted to describe a domain by using a squeezed state in quantum field theory. An extended squeeze operator was used to construct the state. In a scalar field theory, the author described a domain that the distributions of the condensate and of the fluctuation are Gaussian. The momentum distribution, chaoticity and correlation length were calculated. It was found that the typical value of the momentum is about the inverse of the domain size, and that the chaoticity reflects the ratio of the size of the squeeze region to that of the coherent region. The results indicate that the quantum state of a domain is surmised by these quantities under the assumption that the distributions are Gaussian. As an example, this method was applied to a pion field, and the momentum distribution and the chaoticity were shown.Comment: 10 pages, 5 figures, a typographical error in the reference is correcte

Parametric amplification with a friction in heavy ion collisions

We study the effects of the expansion of the system and the friction on the parametric amplification of mesonic fields in high energy heavy ion collisions within the linear $\sigma$ model . The equation of motion which is similar to Mathieu equation is derived to describe the time development of classical fields in the last stage of a heavy ion collision after the freezeout time. The enhanced mode is extracted analytically by comparison with Mathieu equation and the equation of motion is solved numerically to examine whether soft modes will be enhanced or not. It is found that the strong peak appears around 267 MeV in the pion transverse momentum distribution in cases with weak friction and high maximum temperature. This enhancement can be extracted by taking the ratio between different modes in the pion transverse momentum distribution.Comment: 10 pages, 9 figures LaTeX: appendix adde

Estimation of the particle-antiparticle correlation effect for pion production in heavy ion collisions

Estimation of the back-to-back pi-pi correlations arising due to evolution of the pionic field in the course of pion production process is given for central heavy nucleus collisions at moderate energies.Comment: 6 LaTeX pages + 5 ps figure

Dynamical Pion Production via Parametric Resonance from Disoriented Chiral Condensate

We discuss a dynamical mechanism of pion production from disoriented chiral condensates (DCC). It leads to an explosive production of pions via the parametric amplification mechanism, which is similar to the reheating mechanism in inflationary cosmology. Classically, it is related with the instability in the solutions of the Mathieu equation and we explore the quantum aspects of the mechanism. We show that nonlinearlities and back reactions can be ignorable for sufficiently long time under the small amplitude approximations of background $\sigma$ oscillations, which may be appropriate for the late stage of nonequilibrium phase transition. It allows us to obtain an explicit quantum state of the produced pions and $\sigma$, the squeezed state of BCS type. Single particle distributions and two-pion correlation functions are computed within these approximations. The results obtained illuminate the characteristic features of multi-pion states produced through the parametric amplification mechanism. In particular, two-pion correlations of various charge combinations contain back-to-back correlations which cannot be masked by the identical particle interference effect.Comment: REVTEX 18 pages and 10 figure

Squeezed Correlations and Spectra for Mass-Shifted Bosons

Huge back-to-back correlations are shown to arise for thermal ensembles of bosonic states with medium-modified masses. The effect is experimentally observable in high energy heavy ion collisions.Comment: 4 pages (RevTex) including 2 eps figures via psfig, published versio

Nonequilibrium evolution in scalar O(N) models with spontaneous symmetry breaking

We consider the out-of-equilibrium evolution of a classical condensate field and its quantum fluctuations for a scalar O(N) model with spontaneously broken symmetry. In contrast to previous studies we do not consider the large N limit, but the case of finite N, including N=1, i.e., plain $\lambda \phi^ 4$ theory. The instabilities encountered in the one-loop approximation are prevented, as in the large-N limit, by back reaction of the fluctuations on themselves, or, equivalently, by including a resummation of bubble diagrams. For this resummation and its renormalization we use formulations developed recently based on the effective action formalism of Cornwall, Jackiw and Tomboulis. The formulation of renormalized equations for finite N derived here represents a useful tool for simulations with realistic models. Here we concentrate on the phase structure of such models. We observe the transition between the spontaneously broken and the symmetric phase at low and high energy densities, respectively. This shows that the typical structures expected in thermal equilibrium are encountered in nonequilibrium dynamics even at early times, i.e., before an efficient rescattering can lead to thermalization.Comment: 31 pages, 19 Figures, LaTeX; extended discussion on the basis of: fluctuations, eff. potential, correlations, analytic calculation of parametric resonance for "pion"_and_ "sigma" field

Nonlinear evolution of the momentum dependent condensates in strong interaction: the ``pseudoscalar laser''

We discuss the relaxation of the scalar and pseudoscalar condensates after a rapid quench from an initial state with fluctuations. If we include not only the zero-mode but also higher modes of the condensates in the classical evolution, we observe parametric amplification of those ``hard'' modes. Thus, they couple nonlinearly to the ``soft'' modes. As a consequence, domains of coherent pi-field emerge long after the initial spinodal decomposition. The momentum-space distribution of pions emerging from the decay of that momentum-dependent condensate is discussed.Comment: 6 Pages, REVTEX, 8 Figures; one reference and one figure adde