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Title: Nonequilibrium Chiral Dynamics and Two-Particle Correlations in the Time-Dependent Variational Approach with Squeezed States

Abstract

We study the dynamics of chiral phase transition in the O(4) linear sigma model by using the time-dependent variational approach with squeezed states. Our numerical simulations show that large domains of the disoriented chiral condensate (DCC) are formed through the mode-mode correlation. We also present a result of an analysis of the two-particle correlation function for the pion fields, which reflects unique nature of the squeezed states. In particular, we will show that the chaoticity parameter is not close to zero even if DCC domains are produced.

Authors:
 [1];  [2];  [3]
  1. Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047 (Japan)
  2. Department of Physics, Osaka University, Toyonaka 560-0043 (Japan)
  3. Physics Division, Faculty of Science, Kochi University, Kochi 780-8520 (Japan)
Publication Date:
OSTI Identifier:
20800150
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 828; Journal Issue: 1; Conference: 35. internationals symposium on multiparticle dynamics; Workshop on particle correlations and femtoscopy, Kromeriz (Czech Republic), 9-17 Aug 2005; Other Information: DOI: 10.1063/1.2197481; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHIRAL SYMMETRY; CHIRALITY; COMPUTERIZED SIMULATION; CORRELATION FUNCTIONS; CORRELATIONS; PHASE TRANSFORMATIONS; PIONS; SIGMA MODEL; TIME DEPENDENCE; VARIATIONAL METHODS

Citation Formats

Ikezi, N., Asakawa, M., and Tsue, Y. Nonequilibrium Chiral Dynamics and Two-Particle Correlations in the Time-Dependent Variational Approach with Squeezed States. United States: N. p., 2006. Web. doi:10.1063/1.2197481.
Ikezi, N., Asakawa, M., & Tsue, Y. Nonequilibrium Chiral Dynamics and Two-Particle Correlations in the Time-Dependent Variational Approach with Squeezed States. United States. doi:10.1063/1.2197481.
Ikezi, N., Asakawa, M., and Tsue, Y. Tue . "Nonequilibrium Chiral Dynamics and Two-Particle Correlations in the Time-Dependent Variational Approach with Squeezed States". United States. doi:10.1063/1.2197481.
@article{osti_20800150,
title = {Nonequilibrium Chiral Dynamics and Two-Particle Correlations in the Time-Dependent Variational Approach with Squeezed States},
author = {Ikezi, N. and Asakawa, M. and Tsue, Y.},
abstractNote = {We study the dynamics of chiral phase transition in the O(4) linear sigma model by using the time-dependent variational approach with squeezed states. Our numerical simulations show that large domains of the disoriented chiral condensate (DCC) are formed through the mode-mode correlation. We also present a result of an analysis of the two-particle correlation function for the pion fields, which reflects unique nature of the squeezed states. In particular, we will show that the chaoticity parameter is not close to zero even if DCC domains are produced.},
doi = {10.1063/1.2197481},
journal = {AIP Conference Proceedings},
number = 1,
volume = 828,
place = {United States},
year = {Tue Apr 11 00:00:00 EDT 2006},
month = {Tue Apr 11 00:00:00 EDT 2006}
}
  • Explicitly time dependent methods for semiclassical dynamics are explored using variational principles. The Dirac--Frenkel--McLachlan variational principle for the time dependent Schrodinger equation and a variational correction procedure for wavefunctions and transition amplitudes are reviewed. These variational methods are shown to be promising tools for the solution of semiclassical problems where the correspondence principle, classical intuition, or experience suggest reasonable trial forms for the time dependent wavefunction. Specific trial functions are discussed for several applications, including the curve crossing problem. The useful semiclassical content of the time-dependent Hartree approximation is discussed. Procedures for the variational propagation of density matrices are alsomore » derived. (AIP)« less
  • In this paper we use the Lie algebra of space-time symmetries to construct states which are solutions to the time-dependent Schr{umlt o}dinger equation for systems with potentials V(x,{tau})=g{sup (2)}({tau})x{sup 2}+g{sup (1)}({tau})x+g{sup (0)}({tau}). We describe a set of number-operator eigenstates states, {l_brace}{Psi}{sub n}(x,{tau}){r_brace}, that form a complete set of states but which, however, are usually not energy eigenstates. From the extremal state, {Psi}{sub 0}, and a displacement squeeze operator derived using the Lie symmetries, we construct squeezed states and compute expectation values for position and momentum as a function of time, {tau}. We prove a general expression for the uncertainty relationmore » for position and momentum in terms of the squeezing parameters. Specific examples, all corresponding to choices of V(x,{tau}) and having isomorphic Lie algebras, will be dealt with in the following paper (II). {copyright} {ital 1997 American Institute of Physics.}« less
  • In this paper, results from the previous paper (I) are applied to calculations of squeezed states for such well-known systems as the harmonic oscillator, free particle, linear potential, oscillator with a uniform driving force, and repulsive oscillator. For each example, expressions for the expectation values of position and momentum are derived in terms of the initial position and momentum, as well as in the ({alpha},z)- and in the (z,{alpha})-representations described in I. The dependence of the squeezed-state uncertainty products on the time and on the squeezing parameters is determined for each system. {copyright} {ital 1997 American Institute of Physics.}
  • Using the transformations from paper I, we show that the Schroedinger equations for (1) systems described by quadratic Hamiltonians, (2) systems with time-varying mass, and (3) time-dependent oscillators all have isomorphic Lie space-time symmetry algebras. The generators of the symmetry algebras are obtained explicitly for each case and sets of number-operator states are constructed. The algebras and the states are used to compute displacement-operator coherent and squeezed states. Some properties of the coherent and squeezed states are calculated. The classical motion of these states is demonstrated. (c) 2000 American Institute of Physics.