Thermalization of an Interacting Quantum Field in the CTP-2PI Next-to-leading-order Large N Scheme

Abstract

In this paper we use an O(N)-invariant scalar field of unbroken symmetry to investigate whether an interacting quantum field at the next-to-leading order Large $N$ approximation may show signs of thermalization. We develop the closed time-path (CTP) two-particle irreducible (2PI) effective action in powers of 1/N, retaining up to next to leading order (O(1)) terms, and write down the corresponding (truncated) Schwinger-Dyson equations for its two point function. We show that in this approximation, the only translation invariant solutions to the Schwinger - Dyson equations are thermal. This provides a useful temperature concept without invoking a heat bath. When combined with the familiar Kadanoff-Baym approach to quantum kinetic theory our result shows that at this order of approximation thermalization can occur, at least if initial conditions are smooth enough that a derivative expansion is valid. Our analytic result provides support for similar claims in recent literature based on numerical evidence.

arXiv commentLatex 31 pages with 10 figures, uses graphicx

References in corpus (32)

• Bottom-up thermalization in heavy ion collisions
• Structure of Resonance in Preheating after Inflation
• From Quantum Field Theory to Hydrodynamics: Transport Coefficients and Effective Kinetic Theory
• Early thermalization at RHIC
• Analytic and Numerical Study of Preheating Dynamics
• Is early thermalization achieved only near midrapidity at RHIC ?
• Non-Equilibrium Quantum Fields in the Large N Expansion
• Far-from-equilibrium dynamics with broken symmetries from the 2PI-1/N expansion
• Thermalization of Quantum Fields from Time-Reversal Invariant Evolution Equations
• Classical aspects of quantum fields far from equilibrium
• Renormalization in Self-Consistent Approximations schemes at Finite Temperature I: Theory
• Hot B violation, color conductivity, and log(1/alpha) effects
• Nonequilibrium Quantum Dynamics Of Disoriented Chiral Condensates
• Dilepton and photon production in the 'hot-glue' scenario
• Nonequilibrium inflaton dynamics and reheating: Back reaction of parametric particle creation and curved spacetime effects
• O(N) Quantum fields in curved spacetime
• Exact and Truncated Dynamics in Nonequilibrium Field Theory
• Dissipation and Decoherence in Mean Field Theory
• Schwinger-Dyson approach to non-equilibrium classical field theory
• Effective theories for real-time correlations in hot plasmas
• Reheating and thermalization in a simple scalar model
• Resumming the large-N approximation for time evolving quantum systems
• Hydrodynamic transport functions from quantum kinetic theory
• Elliptic Flow from a Transversally Thermalized Fireball
• Time evolution of correlation functions in Non-equilibrium Field Theories
• Longitudinal subtleties in diffusive Langevin equations for non-Abelian plasmas
• Non-equilibrium evolution of a `Tsunami': Dynamical Symmetry Breaking
• Exact and approximate dynamics of the quantum mechanical O(N) model
• Transport Theory of Massless Fields
• Dimensional Crossover in the Large N Limit
• Time evolution of correlation functions for classical and quantum anharmonic oscillators
• Dimensional Crossover in the Non-Linear Sigma Model

Cited by in corpus (8)

• From Kadanoff-Baym dynamics to off-shell parton transport
• Decoherence in an Interacting Quantum Field Theory: The Vacuum Case
• From quantum to classical dynamics: The relativistic $O(N)$ model in the framework of the real-time functional renormalization group
• The O(N) linear sigma model at finite temperature beyond the Hartree approximation
• Entropy and Correlators in Quantum Field Theory
• Correlation Entropy of an Interacting Quantum Field and H-theorem for the O(N) Model
• Macroscopic quantum phenomena from the large N perspective
• Nonequilibrium evolution of Phi**4 theory in 1+1 dimensions in the 2PPI formalism