Non-equilibrium Quantum Field Research Articles

Infrared behavior of quasilocal systems at finite temperature.

We adopt the method developed recently for treating the infrared behavior of finite-size and quasilocal systems to study the symmetry behavior of dynamical quantum fields at finite temperature in cosmological spacetimes. We find that for slowly varying fields at high temperature the critical temperature is increased by an amount proportional to the second-order time derivative (``deceleration'') of the background field. This work can be viewed as a preliminary step towards a fuller investigation of critical dynamics in the early Universe involving nonequilibrium quantum fields.

Quasi-particle field in nonequilibrium quantum field theory

A formulation of nonequilibrium theory is presented on the basis of the quasi-particle picture by using the example of a λφ 4-model. A quasi-particle field is constructed and the quasi-particle field equation obtained is shown to have information of a temporally changing quasi-particle state and a Boltzmann-like equation for particle distribution.

Dissipation in quantum fields and semiclassical gravity

We discuss the theoretical and physical meaning of dissipation of background fields due to particle creation and statistical effects in interacting quantum field theories and in semiclassical gravitational theories. We indicate the possible existence of a fluctuation-dissipation relation for non-equilibrium quantum fields as occuring in cosmological particle creation and backreaction processes. We also conjecture that all effective theories, including quantum gravity, could manifest dissipative behavior.

Self-consistent analysis of a thermally dissipative quantum field system: Korenman's model

Using the Schwinger-Keldysh path-ordering method, a favoured method for doing non-equilibrium quantum field theory, Korenman analyzed a simple model from quantum optics. We study the same model using the recently developed non-equilibrium thermo field dynamics (TFD), and make a comparison of these two methods. TFD can deal with time-dependent non-equilibrium situations caused by the initial conditions being out of equilibrium, while Korenman considered a stationary state maintained by an assumed external pumping mechanism. The explicit TFD calculation at one loop level shows the approach of the system to equilibrium which is described by the master equation derived from the self-consistent renormalization condition. Although both of the methods give practically the same dissipative coefficient in this order of approximation, we would find a larger difference between them in a higher order calculation because of the difference of unperturbative propagators. We also briefly consider the inclusion of a simple pumping mechanism for the system in TFD.

A real-time approach to nonequilibrium quantum field theory of relativistic fields

The basic ingredients of a real-time nonequilibrium quantumfield theoretical approach, based on a generalization of thermofield dynamics, are briefly reviewed. In particular, the possible advantages of its application to relativistic models, as the φ4-model for the Higgs field are pointed out. Also the differences between the above approach and others using the Feynman's path integral method are underlined.

Nonequilibrium quantum fields: Closed-time-path effective action, Wigner function, and Boltzmann equation.

This is the first of a series of papers which describe the functional-integral approach to the study of the statistical and kinetic properties of nonequilibrium quantum fields in flat and curved spacetimes. In this paper we treat a system of self-interacting bosons described by \ensuremath{\lambda}${\ensuremath{\varphi}}^{4}$ scalar fields in flat space. We adopt the closed-time-path (CTP or ``in-in'') functional formalism and use a two-particle irreducible (2PI) representation for the effective action. These formalisms allow for a full account of the dynamics of quantum fields, and put the correlation functions on an equal footing with the mean fields. By assuming a thermal distribution we recover the real-time finite-temperature theory as a special case. By requiring the CTP effective action to be stationary with respect to variations of the correlation functions we obtain an infinite set of coupled equations which is the quantum-field-theoretical generalization of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. Truncation of this series leads to dissipative characteristics in the subsystem. In this context we discuss the nature of dissipation in interacting quantum fields.To one-loop order in a perturbative expansion of the CTP effective action, the 2PI formalism yields results equivalent to the leading 1/N expansion for an O(N)-symmetric scalar field. To higher-loop order we introduce a two-time approximation to separate the quantum-field effects of radiative correction and renormalization from the statistical-kinetic effects of collisions and relaxation. In the weak-coupling quasiuniform limit, the system of nonequilibrium quantum fields can subscribe to a kinetic theory description wherein the propagators are represented in terms of relativistic Wigner distribution functions. From a two-loop calculation we derive the Boltzmann equation for the distribution function and the gap equation for the effective mass of the quasiparticles. One can define an entropy function for the quantum gas of quasiparticles which satisfies the H theorem. We also calculate the limits to the validity of the binary collision approximation from a three-loop analysis. The theoretical framework established here can be generalized to nonconstant background fields and for curved spacetimes.

Nonequilibrium quantum field theories

Abstract Combining the Feynman-Vernon influence functional formalism with the real-time formulation of finite-temperature quantum field theories we present a general approach to relativistic quantum field theories out of thermal equilibrium. We clarify the physical meaning of the additional fields encountered in the real-time formulation of quantum statistics and outline diagrammatic rules for perturbative nonequilibrium computations. We derive a generalization of Boltzmann's equation which gives a complete characterization of relativistic nonequilibrium phenomena.

Turbulence theory on the basis of multipoint distribution functions

Abstract Systematic methods are developed for deriving closed approximate equations for probability densities of a turbulent velocity field at one and at two points. These methods are based on diagram techniques of non-equilibrium statistical mechanics and quantum field theory. The equations are written down in the weak coupling approximation. Arguments are made that the approximation which is graphically equivalent to the direct-interaction approximation well known in turbulence theory is rather exact when used for deriving closed equations for multipoint distribution functions. Analysis of the equations in the weak coupling approximation in the inertial range shows their compatibility with a local cascade mechanism of energy transfer in wave number space.