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 backreaction 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 backreaction 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 phi^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.

Latex file, 44 pages, 3 .eps figures. To appear in Phys. Rev. D. Improved presentation and references added

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• Dynamical behavior of spatially inhomogeneous relativistic $\lambda {\varphi }^4$ quantum field theory in the Hartree approximation
• Kinks in the Hartree approximation
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• A simple theory for quantum quenches in the ANNNI model
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• An O(N) symmetric extension of the Sine-Gordon Equation
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• One-loop results for kink and domain wall profiles at zero and finite temperature
• Fluid Dynamics of Relativistic Quantum Dust
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• Out of equilibrium O (N) linear-sigma system - Construction of perturbation theory with gap- and Boltzmann-equations
• Domain Walls Out of Equilibrium
• The Effect of low Momentum Quantum Fluctuations on a Coherent Field Structure