How Phase Transitions Induce Classical Behaviour

Abstract

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. 03.70.+k, 05.70.Fh, 03.65.Yz

Decoherence of domains and defects at phase transitions

“…We see that decoherence arises so quickly in this event, that it is negligible in comparison to decoherence due to field fluctuations in the way defined in our previous papers.The standard big bang cosmological model of the early universe, with its period of rapid cooling, gives a strong likelihood of phase transitions, with concomitant symmetry breaking. This paper is a further paper in a sequence by ourselves and collaborators [1,2,3] in which we explore the way in which such phase transitions naturally take us from a quantum to classical description of the universe.That (continuous) transitions can lead rapidly to classical behaviour is not surprising. Classical behaviour has two attributes.…”

“…Having seen that the decoherence functional approach gives identical conclusions to the solution of master equations, the new work in this letter is to evaluate the IF for different field configurations which, from the point of view of the Master equation, would be much more taxing analytically. Instead of the classical solutions used before [1,3], in which the field is spread in an infinite chequer-board through space, here we are concerned with a different field configuration; a localized domain wall.…”

“…In fact, rather than consider a whole chequer-board of domains as in [1,2,3], we can restrict ourselves to two adjacent domains with boundary given by (25). Consider the simple case where the difference between walls is given by φ + f = φ − f −ǫ, with ǫ a small fluctuation around the final value of the field configuration.…”

Dissipation and vacuum selection

“…PoS(JHW2005)020 namical evolution of the fields. These equations have been previously used in a relativistic context to study non-equilibrium phenomena in cosmological phase transition [5,6,7]. There are known limitations to the use of these equations, nevertheless they provide an economic and qualitative good description of the different processes involved in the dynamic evolution of the fields where the coupling to the heat bath is expressed by rapidly fluctuating fields and the dissipation effects are expressed by viscosity terms.…”

Role of dissipation in biasing the vacuum selection in quantum field theory at finite temperature

“…Our simulations are governed by phenomenological Langevin equations describing the dynamical evolution of the fields. These equations have been previously used in a relativistic context to study non-equilibrium phenomena in cosmological phase transition [6,7,8]. There are known limitations to the use of these equations which we discuss in Sect.…”