Emergence of Classicality in Quantum Phase Transitions

We show that classicality emerges during quantum phase transitions due to parametric interactions without coupling to environments. The Wigner functions are explicitly calculated for the Gaussian vacuum, number, and thermal states of a free scalar field that describes the spinodal instability regime. The Wigner functions are sharply peaked around their classical trajectories during the phase transition and exhibit classical correlation only for unstable long wavelength modes but retain quantum coherence for short wavelength modes. Thus classicality emerges from the quantum evolution of phase transitions without a classical order parameter. We define a quantal ordering parameter that is linear in the field variable and satisfies the classical field equation