Out-of-equilibrium dynamics of \phi^4 QFT in finite volume

TL;DR

This paper investigates the out-of-equilibrium dynamics of the      model in finite volume, revealing that zero-mode fluctuations do not grow macroscopically and that long-wavelength fluctuations scale with system size, indicating different infrared properties from equilibrium.

Contribution

It provides a detailed analysis of the      model out of equilibrium, highlighting the limitations of the Hartree-Fock approximation and its implications for dynamical infrared behavior.

Findings

Zero-mode quantum fluctuations do not grow macroscopically large from microscopic initial conditions.

Long-wavelength fluctuations scale with the linear size of the system out of equilibrium.

No evidence of dynamical Bose-Einstein condensation in the studied model.

Abstract

The $\lambda \phi^4$ model in a finite volume is studied in the infinite $N$ limit and within a non-gaussian Hartree-Fock approximation both at equilibrium and out of equilibrium, with particular attention to certain fundamental features of the broken symmetry phase. The numerical solution of the dynamical evolution equations show that the zero-mode quantum fluctuations cannot grow macroscopically large starting from microscopic initial conditions. Thus we conclude that there is no evidence for a dynamical Bose-Einstein condensation. On the other hand, out of equilibrium the long-wavelength fluctuations do scale with the linear size of the system, signalling dynamical infrared properties quite different from the equilibrium ones characteristic of the same approximation schemes. This result suggests the cause, and the possible remedy, of some unlikely features of the application to out--of--equilibrium dynamics of the standard HF factorization scheme, which coincides with the gaussian restriction of our Hartree--Fock approximation.