Disoriented chiral condensate in presence of dissipation and noise

We demonstrate that semiclassical fluctuations, their relaxation, and the chiral phase transition are automatically incorporated in the numerical simulations of the classical equations of motion in the linear $\sigma$-model when longitudinal and transverse expansions are included. We find that domains of disoriented chiral condensate with 4--5 fm in size can form through a quench while an annealing leads to domains of smaller sizes. We also demonstrate that quenching cannot b...

We address the issue of whether a region of disordered chiral condensate (DCC), in which the chiral condensate has components along the pion directions, can form. We consider a system going through the chiral phase transition either via a quench, or via relaxation of the high temperature phase to the low temperature one within a given time scale (of order $\sim 1 \rm{fm/c}$). We use a density matrix based formalism that takes both thermal and quantum fluctuations into acc...

I present a summary of recent work \cite{BRS} where we describe the time-evolution of a region of disoriented chiral condensate via Langevin field equations for the linear $\sigma$ model. We analyze the model in equilibrium, paying attention to subtracting ultraviolet divergent classical terms and replacing them by their finite quantum counterparts. We use results from lattice gauge theory and chiral perturbation theory to fix nonuniversal constants. The result is a ultraviol...

First, the chiral phase transition at nonzero temperature and baryon chemical potential is studied at mean field level in the sigma model that includes quark degrees of freedom explicitly. For small bare quark masses the critical point separating the first order phase transition line and the smooth crossover region is determined, and the spinodal lines are drawn. Adiabatic lines are computed showing that the critical point does not serve as focusing point in the adiabatic exp...

We apply the canonical quantum field theory based on the Liouville-von Neumann equation to the nonequilibrium linear sigma model. Particular emphasis is put on the mechanism for domain growth of disoriented chiral condensates due to long wavelength modes and its scaling behavior. Scattering effects, decoherence and emergence of order parameter are also discussed beyond the Hartree approximation.

We argue that disoriented chiral condensate (DCC) domains are not well defined for temperatures above the Ginzburg temperature $T_G$ ($\simeq 0.7 T_c$). Above $T_G$, the dynamics of DCC domains is dominated by thermal fluctuations leading to fluctuating orientation of the chiral field in a given domain. It implies that DCC domains may form even in relatively lower energy collisions where the temperature only reaches $T_G$, and never rises to $T_c$. It also means that detectio...

A simple and consistent real time analysis of the long-wavelength chiral condensate fields in the background of hard thermal modes is presented in the framework of the linear sigma model. Effective evolution equations are derived for the inhomogeneous condensate fields coupled to a heat bath. Multiple effects of the thermal background on the disoriented chiral condensate are studied using linear response theory. We determine the temperature dependence of the equilibrium conde...

Approximate mean-field equations of motion for the classical chiral field are developed within the linear sigma model by means of a Hartree factorization. Both the approximate and the unapproximated equations of motion are augmented with a Rayleigh cooling term to emulate a uniform expansion, thereby allowing the extraction of observables relevant to the detection of disoriented chiral condensates, specifically the pion power spectrum, the pion correlation function, and the d...

We use the linear $\sigma$ model to analyse the dynamics of a disoriented chiral condensate. For idealized boundary conditions appropriate to high energy collisions, the problem can be reduced to a one dimensional one. The evolution of the chiral state is then that of a simple dynamical system and can be studied analytically.

Using the influence functional formalism, classical equations of motion for the O(N) model are derived in the presence of a heat bath, in both the symmetric phase as well as the phase of spontaneously broken symmetry. The heat bath leads to dissipation and fluctuation terms in the classical equations of motion, which are explicitly computed to lowest order in perturbation theory. In the broken phase these terms are found to be large for the sigma field, even at zero temperatu...