Quantum fields out of thermal equilibrium

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Abstract
The isoentropic, but energy-nonconserving, time evolution of mixed quantum states is studied in quantum mechanics and quantum field theory. A variational principle, which gives the Liouville–von Neumann equation, is implemented approximately by making a Gaussian Ansatz for the density matrix. The dynamical equations governing the parameters that define the Ansatz satisfy equations variously analogous to the Schrödinger equation and to mechanical problems. Interesting nonequilibrium evolution is found in special cases, as, for example, when the analog Schrödinger equation gives rise to reflectionless transmission. For field theory in an external, time-dependent metric we obtain equations that were previously derived in the many-field (spherical-model) limit.