Dynamics of phase transition in (3+1) dimensional scalar $\phi^4$ theory

TL;DR

This paper investigates the non-equilibrium quantum dynamics of second order phase transitions in (3+1)D scalar $^4$ theory using a variational approach, revealing how quenching affects vacuum structure and correlation lengths.

Contribution

It introduces a variational approximation method to study out-of-equilibrium dynamics and analyzes the effects of mass-squared quenching on phase transition behavior in scalar field theory.

Findings

Quenching of mass-squared induces nontrivial second order phase transitions.

Correlation length dynamics depend on the time variation of mass-squared.

Propagation of spatial correlations persists after phase transition ends.

Abstract

We use the variational approximation with double Gaussian type trial wave-functional approximation, in which we use the square root of the dispersion of the zero-mode wave-function as an order parameter, to study the out of equilibrium quantum dynamics of time-dependent second order phase transitions in (3+1) dimensions. We study the time evolution of symmetric states of scalar $\lambda \phi^4$ theory in several situations by properly treating the effect of the $\lambda\phi^4$ interaction. We also calculate the effective action and the effective potential of the theory with the precarious renormalization. We show that the presence of a quenching of the mass-squared leads to second order phase transition nontrivially since the vacuum structure changes by absorbing the energy required for quenching, even though there is no symmetry breaking in the effective potential of the theory without quenching process. We also calculate the equal time correlation function, and then evaluate the correlation length as a function of the mass-squared. The time dependence of the correlation length varies depending on how the mass-squared changes in time. For constant mass-squared it gives the classical Cahn-Allen relation, and it leads to different relations for other time-dependence of the mass-squared. We also show that there exists a propagating spatial correlation after termination of the phase transition process in addition to the correlation corresponding to the formation and growth of domains.