Onset of classical behaviour after a phase transition

Abstract

We analyze the onset of classical behaviour in a scalar field after a continuous phase transition, in which the system-field, the long wavelength order parameter of the model, interacts with an environment of its own shortwavelength modes. We compute the decoherence time for the system-field modes from the master equation and compare it with the other time scales of the model. Within our approximations the decoherence time is in general the smallest dynamical time scale. Demanding diagonalisation of the decoherence functional produces identical results. The inclusion of other environmental fields makes diagonalisation occur even earlier.

Nonequilibrium Quantum Field Theory

“…As we have already remarked, at early times the system field may be described as an inverted harmonic oscillator. The evolution is then well approximated by an ensemble of classical trajectories, but there remains the question of whether two different classical histories are consistent in the Gell-Mann-Hartle sense [RivLom05,LoRiVi07].…”

“…We shall ask what is the minimum speed difference at the initial time that ensures consistency by t = t sp . If this minimum difference is much smaller than the natural spread ∼ (T c /V ) 1/2 , then the conclusion that decoherence is faster than spinodal decomposition is upheld [RivLom05]. We will calculate the decoherence functional to lowest nontrivial order (two vertices) for large N .…”