Nonequilibrium dynamics of quantum fields

We examine the nonequilibrium dynamics of a self-interacting $\lambda\phi^4$ scalar field theory. Using a real time formulation of finite temperature field theory we derive, up to two loops and $O(\lambda^2)$, the effective equation of motion describing the approach to equilibrium. We present a detailed analysis of the approximations used in order to obtain a Langevin-like equation of motion, in which the noise and dissipation terms associated with quantum fluctuations obey a...

We study the approach to equilibrium for a scalar field which is coupled to a large thermal bath. Our analysis of the initial value problem is based on Kadanoff-Baym equations which are shown to be equivalent to a stochastic Langevin equation. The interaction with the thermal bath generates a temperature-dependent spectral density, either through decay and inverse decay processes or via Landau damping. In equilibrium, energy density and pressure are determined by the Bose-Ein...

We study the non-equilibrium dynamics of a symmetry restoring phase transition in a scalar field theory, the ``system'', linearly coupled to another scalar field taken as a ``heat bath''. The ``system'' is initially in an ordered low temperature phase, and the heat bath is at a temperature close to the critical temperature for the system. We estimate the time at which the phase transition to the disordered (symmetric) phase takes place. We derive, and integrate the one-loop e...

The nonperturbative real-time evolution of quantum fields out of equilibrium is often solved using a mean-field or Hartree approximation or by applying effective action methods. In order to investigate the validity of these truncations, we implement similar methods in classical scalar field theory and compare the approximate dynamics with the full nonlinear evolution. Numerical results are shown for the early-time behaviour, the role of approximate fixed points, and thermaliz...

We study the dynamics of the oscillating gauged scalar field in a thermal bath. A Langevin type equation of motion of the scalar field, which contains both dissipation and fluctuation terms, is derived by using the real-time finite temperature effective action approach. The existence of the quantum fluctuation-dissipation relation between the non-local dissipation term and the Gaussian stochastic noise terms is verified. We find the noise variables are anti-correlated at equa...

We present lattice simulations of nonequilibrium quantum fields in Minkowskian space-time. Starting from a non-thermal initial state, the real-time quantum ensemble in 3+1 dimensions is constructed by a stochastic process in an additional (5th) ``Langevin-time''. For the example of a self-interacting scalar field we show how to resolve apparent unstable Langevin dynamics, and compare our quantum results with those obtained in classical field theory. Such a direct simulation m...

We review recent developments for the description of far-from-equilibrium dynamics of quantum fields and subsequent thermalization.

We consider the non-equilibrium dynamics of a real quantum scalar field. We show the formal equivalence of the exact evolution equations for the statistical and spectral two-point functions with a fictitious Langevin process and examine the conditions under which a local Markovian dynamics is a valid approximation. In quantum field theory, the memory kernel and the noise correlator typically exhibit long time power laws and are thus highly non-local, thereby questioning the p...

The time evolution of O(N) symmetric lambda Phi^4 scalar field theory is studied in the large N limit. In this limit the <Phi> mean field and two-point correlation function <Phi Phi> evolve together as a self-consistent closed Hamiltonian system, characterized by a Gaussian density matrix. The static part of the effective Hamiltonian defines the True Effective Potential U_eff for configurations far from thermal equilibrium. Numerically solving the time evolution equations for...

The emergence of an effective field theory out of equilibrium is studied in the case in which a light field --the system-- interacts with very heavy fields in a finite temperature bath. We obtain the reduced density matrix for the light field, its time evolution is determined by an effective action that includes the \emph{influence action} from correlations of the heavy degrees of freedom. The non-equilibrium effective field theory yields a Langevin equation of motion for the...