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

Abstract

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 ...

Effects of mode-mode and isospin-isospin correlations on domain formation of disoriented chiral condensates

“…In this process, however, the change of the effective potential is so rapid that the order parameter cannot follow the change and remains around the origin, where the minimum of the effective potential is in the chirally symmetric phase. [1,2,10]. Namely, in the quench scenario, the mean of the chiral fields as well as the correlation of the fields are the same as those before the sudden cooling (quenching), but only the sizes of the fluctuations of the mean fields and their conjugate fields are quenched.…”

“…For the mean fields, we have used the same prescription for the initial condition as in Refs. [10,14]: at each grid site, the mean field variables for the chiral fields and their conjugate variables C a ( x, 0) and D a ( x, 0) are randomly distributed with the Gaussian weights with the following parameters,…”

“…We use the Gaussian width δ = 0.19v, which is the same value which has been taken in Ref. [10]. This value is so chosen that the fluctuation is small enough and the chiral symmetry is spontaneously broken.…”

“…Recently, it was explicitly shown that DCC domains are formed in quantum calculation for the first time in the case of 1+1 dimensional geometry [10]. In that calculation, the mode-mode correlations are explicitly taken into account and no translational invariance was assumed.…”

Variational Approach to the Chiral Phase Transition in the Linear Sigma Model

“…33) Thus, as another future problem, it may be important to understand the dynamical chiral phase transition in the several situations, for example, in the quench scenario, 34) in the context of the high energy heavy ion collisions.…”