Evolution of inhomogeneous condensates: Self-consistent variational approach

Abstract

We establish a self-consistent variational framework that allows us to study numerically the non-equilibrium evolution of non-perturbative inhomogeneous field configurations including quantum back reaction effects. After discussing the practical merits and disadvantages of different approaches we provide a closed set of local and renormalizable update equations that determine the dynamical evolution of inhomogeneous condensates and can be implemented numerically. These incorporate self-consistently the back reaction of quantum fluctuations and particle production. This program requires the solution of a self-consistent inhomogeneous problem to provide initial Cauchy data for the inhomogeneous condensates and Green's functions. We provide a simple solvable ansatz for such an initial value problem for the sine-Gordon and ${\ensuremath{\varphi}}^{4}$ quantum field theories in one spatial dimension. We compare exact known results of the sine-Gordon model to this simple ansatz. We also study the linear sigma model in the large $N$ limit in three spatial dimensions as a microscopic model for pion production in ultrarelativistic collisions. We provide a solvable self-consistent ansatz for the initial value problem with cylindrical symmetry. For this case we also obtain a closed set of local and renormalized update equations that can be numerically implemented. A novel phenomenon of spinodal instabilities and pion production arises as a result of a Klein paradox for large amplitude inhomogeneous condensate configurations.