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arXiv:hep-ph/0102152 · Physics Letters B

Classical behaviour after a phase transition

F.C. Lombardo, F.D. Mazzitelli, R.J. Rivers

Published Dec 1, 2001• 19 citations
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Abstract

We analyze the onset of classical behaviour after a second-order phase transition by considering a scalar field theory in which the system-field interacts with its environment, represented both by further fields and by its own short-wavelength modes. Within our approximations we see that the long-wavelength modes have become classical by the time that the transition has been first implemented (the spinodal time).

DOI
10.1016/s0370-2693(01)01358-2

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We analyze the onset of classical behaviour after a second-order phase transition by considering a scalar field theory in which the system-field interacts with its environment, represented both by further fields and by its own short-wavelength modes. Within our approximations we see that the long-wavelength modes have become classical by the time that the transition has been first implemented (the spinodal time).
We analyze the onset of classical behaviour after a second-order phase transition in quantum field theory. We consider a scalar theory in which the system-field interacts with its environment, represented both by further scalar fields and by its own short-wavelength modes. We compute the decoherence time for the system-field modes and compare it with the other time scales of the model. Within our approximations we see that the long-wavelength modes have decohered by the time that the transition has been first implemented (the spinodal time)
We analyze the onset of classical field configurations after a phase transition. Firstly, we motivate the problem by means of a toy model in quantum mechanics. Subsequently, we consider a scalar field theory in which the system-field interacts with its environment, represented both by further scalar fields and by its own short-wavelength modes. We show that, for very rapid quenches, the order parameter can be treated classically by the time that it has achieved its ground state values (spinodal time).
We continue the analysis of 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 short-wavelength modes and other fields, neutral and charged, with which it is expected to interact. We compute the decoherence time for the system-field modes from the master equation and directly from the decoherence functional (with identical results). In simple circumstances the order parameter field is classical by the time the transition is complete. © 2005 Springer Science+Business Media, Inc.
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.
We show that the long wavelength modes of a field become classical during a second order phase transition because of the interaction with the short wavelength modes of the field. In a massive scalar field model the number and thermal states of long wavelength modes, whose Wigner functions are sharply peaked around the classical trajectories during the phase transition, exhibit only classical correlation without achieving quantum decoherence. In a linearly coupled scalar field model, the long wavelength modes are shown to effectively achieve quantum decoherence because of the mode mixing. Finally we define a quantal ordering parameter that is linear in the field variable and satisfies the classical field equation.