Exact and Truncated Dynamics in Nonequilibrium Field Theory

Abstract

Nonperturbative dynamics of quantum fields out of equilibrium is often described by the time evolution of a hierarchy of correlation functions, using approximation methods such as Hartree, large N, and nPI-effective action techniques. These truncation schemes can be implemented equally well in a classical statistical system, where results can be tested by comparison with the complete nonlinear evolution obtained by numerical methods. For a 1+1 dimensional scalar field we find that the early-time behaviour is reproduced qualitatively by the Hartree dynamics. The inclusion of direct scattering improves this to the quantitative level. We show that the emergence of nonthermal temperature profiles at intermediate times can be understood in terms of the fixed points of the evolution equations in the Hartree approximation. The form of the profile depends explicitly on the initial ensemble. While the truncated evolution equations do not seem to be able to get away from the fixed point, the full nonlinear evolution shows thermalization with a (surprisingly) slow relaxation.

30 pages with 12 eps figures, minor changes; to appear in Phys.Rev.D

References in corpus (6)

• On Thermalization in Classical Scalar Field Theory
• Particle Production and Effective Thermalization in Inhomogeneous Mean Field Theory
• Exact and approximate dynamics of the quantum mechanical O(N) model
• Time evolution of correlation functions and thermalization
• Large N Quantum Time Evolution Beyond Leading Order
• Out-of-equilibrium dynamics of large-N ϕ^4 QFT in finite volume

Cited by in corpus (63)

• Prethermalization
• Non-thermal fixed points: effective weak-coupling for strongly correlated systems far from equilibrium
• Prethermalization and universal dynamics in near-integrable quantum systems
• QCD thermalization: Ab initio approaches and interdisciplinary connections
• Controlled nonperturbative dynamics of quantum fields out of equilibrium
• Classical aspects of quantum fields far from equilibrium
• n-Particle irreducible effective action techniques for gauge theories
• Thermalization of fermionic quantum fields
• Nonequilibrium time evolution of the spectral function in quantum field theory
• Bottom-up isotropization in classical-statistical lattice gauge theory
• Tachyonic preheating using 2PI-1/N dynamics and the classical approximation
• Information Content of Spontaneous Symmetry Breaking
• Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments
• Equilibration in phi^4 theory in 3+1 dimensions
• Hydrodynamics Near a Chiral Critical Point
• Dynamical crossovers in prethermal critical states
• Nonperturbative dynamical many-body theory of a Bose-Einstein condensate
• Prescaling and far-from-equilibrium hydrodynamics in the quark-gluon plasma
• Schwinger-Dyson approach to non-equilibrium classical field theory
• Information-Entropic Signature of the Critical Point
• Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas
• Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws
• The approach to thermalization in the classical phi^4 theory in 1+1 dimensions: energy cascades and universal scaling
• Resumming the large-N approximation for time evolving quantum systems
• Thermalization in a Hartree Ensemble Approximation to Quantum Field dynamics
• Non-thermal fixed points: Universal dynamics far from equilibrium
• Resonant nucleation of spatio-temporal order via parametric modal amplification
• Low-energy effective theory of non-thermal fixed points in a multicomponent Bose gas
• Resonant Nucleation
• Bubbling the False Vacuum Away
• Prescaling in a far-from-equilibrium Bose gas
• Thermalization of an Interacting Quantum Field in the CTP-2PI Next-to-leading-order Large N Scheme
• Staying Thermal with Hartree Ensemble Approximations
• Nonequilibrium dynamics in the O(N) model to next-to-next-to-leading order in the 1/N expansion
• Bi-directional universal dynamics in a spinor Bose gas close to a non-thermal fixed point
• Ultraviolet cascade in the thermalization of the classical phi^4 theory in 3+1 dimensions
• Primordial cosmic fluctuations for variable gravity
• Classical Limit of Time-Dependent Quantum Field Theory-a Schwinger-Dyson Approach
• Cosmic fluctuations from quantum effective action
• Dynamics of broken symmetry lambda phi^4 field theory
• Amplified Fermion Production from Overpopulated Bose Fields
• On the quantum stability of Q-balls
• Universal dynamics and non-thermal fixed points in quantum fluids far from equilibrium
• On Evolution of Coherent States as Quantum Counterpart of Classical Dynamics
• Thermal effects on slow-roll dynamics
• Effective convergence of the 2PI-1/N expansion for nonequilibrium quantum fields
• Correlation Entropy of an Interacting Quantum Field and H-theorem for the O(N) Model
• Cosmology from pregeometry
• Particle creation and warm inflation
• The Hartree ensemble approximation revisited: The "symmetric phase"
• Many-body chaos near a thermal phase transition
• Stationarity, soft ergodicity, and entropy in relativistic systems
• Spinodal Instabilities and Super-Planckian Excursions in Natural Inflation
• Real-time dynamics of the O(N) model in 1+1 dimensions
• Expanding non homogeneous configurations of the $\lambda {\varphi }^4$ model
• Nonequilibrium Evolution of Correlation Functions: A Canonical Approach
• Shear viscosity of classical Yang-Mills field
• Parallel algorithm with spectral convergence for nonlinear integro-differential equations
• Adiabatic Hydrodynamization and the Emergence of Attractors: a Unified Description of Hydrodynamization in Kinetic Theory
• Non-Equilibrium Large N Yukawa Dynamics: marching through the Landau pole
• Continuum versus periodic lattice Monte Carlo approach to classical field theory
• Ergodic and non-ergodic many-body dynamics in strongly nonlinear lattices
• Renormalized waves and thermalization of the Klein-Gordon equation: What sound does a nonlinear string make?