Nonequilibrium evolution of Phi**4 theory in 1+1 dimensions in the 2PPI formalism

Abstract

We consider the out-of-equilibrium evolution of a classical condensate field and its quantum fluctuations for a Phi**4 model in 1+1 dimensions with a symmetric and a double well potential. We use the 2PPI formalism and go beyond the Hartree approximation by including the sunset term. In addition to the mean field phi=<Phi> the 2PPI formalism uses as variational parameter a time dependent mass M**2(t) which contains all local insertions into the Green function. We compare our results to those obtained in the Hartree approximation. In the symmetric Phi**4 theory we observe that the mean field shows a stronger dissipation than the one found in the Hartree approximation. The dissipation is roughly exponential in an intermediate time region. In the theory with spontaneous symmetry breaking, i.e., with a double well potential, the field amplitude tends to zero, i.e., to the symmetric configuration. This is expected on general grounds: in 1+1 dimensional quantum field theory there is no spontaneous symmetry breaking for T >0, and so there should be none at finite energy density (microcanonical ensemble), either. Within the time range of our simulations the momentum spectra do not thermalize and display parametric resonance bands.

arXiv comment14 pages, 18 encapsulated postscript figures; v2 minor changes, new appendix, accepted for publication in Phys.Rev.D

References in corpus (27)

• Reheating after Inflation
• Analytic and Numerical Study of Preheating Dynamics
• Controlled nonperturbative dynamics of quantum fields out of equilibrium
• Far-from-equilibrium dynamics with broken symmetries from the 2PI-1/N expansion
• Parametric resonance in quantum field theory
• Thermalization of Quantum Fields from Time-Reversal Invariant Evolution Equations
• Classical aspects of quantum fields far from equilibrium
• Nonequilibrium Dynamics of Symmetry Breaking in Lambda Phi^4 Field Theory
• Renormalization in Self-Consistent Approximations schemes at Finite Temperature I: Theory
• Renormalization in Self-Consistent Approximation schemes at Finite Temperature III: Global Symmetries
• Renormalization of Self-consistent Approximation schemes Finite Temperature II: Applications to the Sunset Diagram
• Quantum dynamics of phase transitions in broken symmetry $\lambda {\varphi }^4$ field theory
• Schwinger-Dyson approach to non-equilibrium classical field theory
• Resumming the large-N approximation for time evolving quantum systems
• Asymptotic Dynamics in Scalar Field Theory: Anomalous Relaxation
• On the choice of initial states in nonequilibrium dynamics
• The O(N) linear sigma model at finite temperature beyond the Hartree approximation
• Thermalization of an Interacting Quantum Field in the CTP-2PI Next-to-leading-order Large N Scheme
• Summation and renormalization of bubble graphs to all orders
• Study of the O(N) linear sigma model at finite temperature using the 2PPI expansion
• A 2 Loop 2PPI Analysis of $\lambda {\varphi }^4$ at Finite Temperature
• Nonequilibrium evolution in scalar O(N) models with spontaneous symmetry breaking
• Dynamics of broken symmetry lambda phi^4 field theory
• Out-of-equilibrium dynamics of large-N ϕ^4 QFT in finite volume
• Initial Conditions for Semiclassical Field Theory
• The mass gap and vacuum energy of the Gross-Neveu model via the 2PPI expansion
• Multi-particle States from the Effective Action for Local Composite Operators: Anharmonic Oscillator

Cited by in corpus (11)

• Shear Viscosity in the O(N) Model
• The approach to thermalization in the classical phi^4 theory in 1+1 dimensions: energy cascades and universal scaling
• Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of $\lambda {\varphi }^4$ field theory
• The O(N) linear sigma model at finite temperature beyond the Hartree approximation
• Inertial mechanism: dynamical mass as a source of particle creation
• Counterterm resummation for 2PI-approximation in constant background
• Out-of-equilibrium evolution of quantum fields in the hybrid model with quantum back reaction
• Quantum dynamics of Phi**4 field theory beyond leading order in 1+1 dimensions
• The effect of memory on relaxation in a scalar field theory
• 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
• Out-of-equilibrium quantum fields with conserved charge