Nonequilibrium dynamics of quantum fields

I review some open problems on the ever-growing field of non-equilibrium phase transitions, paying special attention to the formulation of such problems in terms of Langevin equations or, equivalently, field-theoretical descriptions, and their solution using renormalization

We introduce functional methods to study the non-equilibrium dynamics of a quantum massless scalar field at finite temperature in a gravitational field. We calculate the Close Time Path (CTP) effective action and, using its formal equivalence with the influence functional, derive the noise and dissipation kernels of the quantum open system in terms of quantities in thermodynamical equilibrium. Using this fact, we formally prove the existence of a Fluctuation-Dissipation Relat...

The 2PI effective action formalism for quantum fields out of equilibrium is set up in an expanding (Friedmann-Robertson-Walker) background. We write down and solve the evolution equations for a phi^4 model at NLO in a coupling expansion. We comment on issues of renormalization, lattice discretization and the range of applicability of the approach. A number of example calculations are presented, including thermalization and (p)reheating. Generalizations to more complicated sys...

A definition of nonequilibrium free energy $\mathcal{F}_{\textsc{s}}$ is proposed for dynamical Gaussian quantum open systems strongly coupled to a heat bath and a formal derivation is provided by way of the generating functional in terms of the coarse-grained effective action and the influence action. For Gaussian open quantum systems exemplified by the quantum Brownian motion model studied here, a time-varying effective temperature can be introduced in a natural way, and wi...

We present a novel simulation prescription for thermal quantum fields on a lattice that operates directly in imaginary frequency space. By distinguishing initial conditions from quantum dynamics it provides access to correlation functions also outside of the conventional Matsubara frequencies $\omega_n=2\pi n T$. In particular it resolves their frequency dependence between $\omega=0$ and $\omega_1=2\pi T$, where the thermal physics $\omega\sim T$ of e.g.~transport phenomena i...

We study the dynamical evolution of coupled one- and two-point functions of a scalar field in the 2PI framework at the Hartree approximation, including backreaction from out-of-equilibrium modes. We renormalize the 2PI equations of motion in an on-shell scheme in terms of physical parameters. We present the Hartree-resummed renormalized effective potential at finite temperature and critically discuss the role of the effective potential in a non-equilibrium system. We follow t...

We discuss the possibility of defining an emergent local temperature in extended quantum many-body systems evolving out of equilibrium. For the most simple case of free-fermionic systems, we give an explicit formula for the effective temperature in the case of, not necessarily unitary, Gaussian preserving dynamics. In this framework, we consider the hopping fermions on a one-dimensional lattice submitted to randomly distributed projective measurements of the local occupation ...

We review recent developments for the description of nonequilibrium quantum fields, continuing hep-ph/0302210.

We calculate the far-from-equilibrium dynamics and thermalization both for the quantum and the classical O(N)--model. The early and late-time behavior can be described from the 2PI--loop expansion for weak couplings or the nonperturbative 2PI--1/N expansion of the effective action beyond leading order. A comparison with exact simulations in 1+1 dimensions in the classical limit shows that the 2PI--1/N expansion at next-to-leading order gives quantitatively precise results alr...

Conventional transport theory is not really applicable to non-equilibrium systems which exhibit strong quantum effects. We present two different approaches to overcome this problem. Firstly we point out how transport equations may be derived that incorporate a nontrivial spectral function as a typical quantum effect, and test this approach in a toy model of a strongly interacting degenerate plasma. Secondly we explore a path to include non-equilibrium effects into quantum fie...