The time-evolution of quantum meson fields is investigated in the linear sigma model by means of the time-dependent variational approach with a squeezed state. The chiral condensate, which is a mean field of the quantum meson fields, and quantum fluctuations around it are treated self-consistently in this approach. The attention is paid to the description of the relaxation process of the chiral condensate, where the energy stored in the mean field configuration flows to the fluctuation modes. It is shown that the quantum fluctuations play an important role in describing this relaxation process.
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.The possibility of the formation of the disoriented chiral condensate (DCC) in high energy heavy ion collisions has been extensively studied with various methods. In classical approximation [1,2], it has been shown that the amplification of long wavelength modes of the pion fields takes place when the system starts with the nonequilibrium initial condition, quench initial condition [1,2]. In addition to the amplification, spatial correlation of the fields has been also shown to grow.Although the classical approximation is expected to work well in incorporating nonequilibrium aspects of the system when pion density is large, it is still desirable to include quantum effects. In fact, investigations in this direction have been also carried out extensively with the Hartree approximation, the large N approximation, and so on [3,4]. In most of the previous studies which include quantum effects, however, it has been assumed that the system is spatially homogeneous. Problems such as insufficient thermalization at late times and impossibility to describe domain structures have been recognized. It has not been conclusive whether there is a chance for the correlations to grow through nonequilibrium time evolution.There are at least two ways for possible improvement. One is to include higher order quantum corrections and the other is to accommodate spatial inhomogeneity. We will pursue the latter in this paper. Recently, the dynamics of spatially inhomogeneous system has been studied by several groups quantum mechanically [5,6,7,8] and it has been shown that the thermalization of the quantum fields can occur. In these works, the Gaussian approximation, in which the Green's functions are assumed to be diagonal in momentum space, has been adopted because of computational reasons. Physically, it corresponds to ignoring correlations between modes with different momenta, and under the approximation different modes can interact only through the mean fields. However, it is possible that the direct coupling of modes through the offdiagonal correlations is important for the time evolution of the system when the system does not possess translational invariance. To see if such an effect is substantial, we study the dynamics of chiral phase transition in spatially inhomogeneous systems with off-diagonal components of the Green's function in momentum space fully taken into account.In this paper, we take the O(4) linear sigma model as a low energy effective theory of QCD and apply the method of the time dependent variational approach (TDVA) with squeezed states. This method was originally developed by Jackiw and Kerman ...
The effects of mode-mode and isospin-isospin correlations on nonequilibrium chiral dynamics are investigated by using the method of the time dependent variational approach with squeezed states as trial states. Our numerical simulations show that large domains of the disoriented chiral condensate (DCC) are formed due to the combined effect of the mode-mode and isospin-isospin correlations. Moreover, it is found that, when the mode-mode correlation is included, the DCC domain formation is accompanied by the amplification of the quantum fluctuation, which implies the squeezing of the state. However, neither the DCC domain formation nor the amplification of the quantum fluctuation is observed if only the isospin-isospin correlation is included. This suggests that the mode-mode coupling plays a key role in the DCC domain formation.
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