Nonequilibrium evolution in scalar O(N) models with spontaneous symmetry breaking

Abstract

We consider the out-of-equilibrium evolution of a classical condensate field and its quantum fluctuations for a scalar O(N) model with spontaneously broken symmetry. In contrast to previous studies we do not consider the large N limit, but the case of finite N, including N=1, i.e., plain $\lambda {\varphi }^4$ theory. The instabilities encountered in the one-loop approximation are prevented, as in the large-N limit, by back reaction of the fluctuations on themselves, or, equivalently, by including a resummation of bubble diagrams. For this resummation and its renormalization we use formulations developed recently based on the effective action formalism of Cornwall, Jackiw and Tomboulis. The formulation of renormalized equations for finite N derived here represents a useful tool for simulations with realistic models. Here we concentrate on the phase structure of such models. We observe the transition between the spontaneously broken and the symmetric phase at low and high energy densities, respectively. This shows that the typical structures expected in thermal equilibrium are encountered in nonequilibrium dynamics even at early times, i.e., before an efficient rescattering can lead to thermalization.

31 pages, 19 Figures, LaTeX; extended discussion on the basis of: fluctuations, eff. potential, correlations, analytic calculation of parametric resonance for "pion"_and_ "sigma" fields

References in corpus (6)

• Nonequilibrium time evolution of the spectral function in quantum field theory
• Schwinger-Dyson approach to non-equilibrium classical field theory
• Dynamics of coupled bosonic systems with applications to preheating
• A 2 Loop 2PPI Analysis of $\lambda {\varphi }^4$ at Finite Temperature
• Pion Production by Parametric Resonance Mechanism with Quantum Back Reactions
• Pion production in nonequilibrium Chiral perturbation Theory

Cited by in corpus (20)

• Symmetry Breaking and False Vacuum Decay after Hybrid Inflation
• Chern-Simons production during preheating in hybrid inflation models
• Low-cost fermions in classical field simulations
• 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
• Non-equilibrium dynamics of a scalar field with quantum backreaction
• Goldstone excitations from spinodal instability
• Macroscopic quantum phenomena from the large N perspective
• Tachyonic production of dark relics: a non-perturbative quantum study
• Nonequilibrium evolution of Phi**4 theory in 1+1 dimensions in the 2PPI formalism
• Out-of-equilibrium evolution of quantum fields in the hybrid model with quantum back reaction
• The renormalized and Renormalization-Group invariant Hartree-Fock approximation
• Off-equilibrium dynamics of the primordial perturbations in the inflationary universe: the O(N) model
• The 2PI finite temperature effective potential of the O(N) linear sigma model in 1+1 dimensions, at next-to-leading order in 1/N
• Nonequilibrium Evolution of Correlation Functions: A Canonical Approach
• Effective field theory of waterfall in hybrid inflation
• Nonequilibrium dynamics of the O(N) linear sigma model
• Tunneling in a quantum field theory on a compact one-dimensional space
• Improved Hartree--Fock resummations and spontaneous symmetry breaking
• Linear sigma model at finite temperature