An improved time-dependent Hartree-Fock approach for scalar ϕ^4 QFT

Abstract

The $\lambda {\varphi }^4$ model in a finite volume is studied within a non-gaussian Hartree-Fock approximation (tdHF) both at equilibrium and out of equilibrium, with particular attention to the structure of the ground state and of certain dynamical features in the broken symmetry phase. The mean-field coupled time-dependent Schroedinger equations for the modes of the scalar field are derived and the suitable procedure to renormalize them is outlined. A further controlled gaussian approximation of our tdHF approach is used in order to study the dynamical evolution of the system from non-equilibrium initial conditions characterized by a uniform condensate. We find that, during the slow rolling down, the long-wavelength quantum fluctuations do not grow to a macroscopic size but do scale with the linear size of the system, in accordance with similar results valid for the large $N$ approximation of the O(N) model. This behavior undermines in a precise way the gaussian approximation within our tdHF approach, which therefore appears as a viable mean to correct an unlikely feature of the standard HF factorization scheme, such as the so-called ``stopping at the spinodal line'' of the quantum fluctuations. We also study the dynamics of the system in infinite volume with particular attention to the asymptotic evolution in the broken symmetry phase. We are able to show that the fixed points of the evolution cover at most the classically metastable part of the static effective potential.

Accepted for publication on Phys. Rev. D

References in corpus (1)

• Out-of-equilibrium dynamics of large-N ϕ^4 QFT in finite volume

Cited by in corpus (11)

• Nonequilibrium Quantum Dynamics of Second Order Phase Transitions
• The O(N) linear sigma model at finite temperature beyond the Hartree approximation
• Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase
• Nonequilibrium evolution and symmetry structure of the large-N ${\Phi }^4$ model at finite temperature
• Nonequilibrium evolution in scalar O(N) models with spontaneous symmetry breaking
• The renormalized and Renormalization-Group invariant Hartree-Fock approximation
• Expanding non homogeneous configurations of the $\lambda {\varphi }^4$ model
• Machian Classical and Semiclassical Emergent Time
• Tunneling in a quantum field theory on a compact one-dimensional space
• Improved Hartree--Fock resummations and spontaneous symmetry breaking
• Collective coordinate descriptions of a kink in a driven-damped ${\varphi }^4$ model