On the treatment of initial correlations in quantum field theory of non-equilibrium states

Thomas-Paul Hack, Rainer Verch

Non-equilibrium steady states (NESS) describe particularly simple and stationary non-equilibrium situations. A possibility to obtain such states is to consider the asymptotic evolution of two infinite heat baths brought into thermal contact. In this work we generalise corresponding results of Doyon~et.~al. (J.\ Phys.\ A 18 (2015) no.9) for free Klein-Gordon fields in several directions. Our analysis is carried out directly at the level of correlation functions and in the algebraic approach to QFT. We discuss non-trivial chemical potentials, condensates, inhomogeneous linear models and homogeneous interacting ones. We shall not consider a sharp contact at initial time, but a smooth transition region. As a consequence, the states we construct will be of Hadamard type, and thus sufficiently regular for the perturbative treatment of interacting models. Our analysis shows that perturbatively constructed interacting NESS display thermodynamic properties similar to the ones of the NESS in linear models. In particular, perturbation theory appears to be insufficient to describe full thermalisation in non-linear QFT. Notwithstanding, we find that the NESS for linear and interacting models is stable under small perturbations, which is one of the characteristic features of equilibrium states.

Da-Shin Lee

Bedřich Velicky´, Anděla Kalvová, and V Spicka

Construction of the electron quantum transport equations from Non-Equilibrium Green's Functions is presently based on Reconstruction Theorems, reducing full description of a non-equilibrium system to a dynamic theory in terms of one-particle quantities. This approach, stemming from the original Kadanoff-Baym Ansatz, and based on a suitably renormalized NGF formalism, can be brought to a close parallel with the Time Dependent Density Functional Theory. This concerns, in particular, the role of correlations at a finite initial time. A universal treatment of these initial conditions is possible for the switch-on states, while more general initial states have so far to be treated individually.

D. Boyanovsky, Hector J. de Vega, R. Holman

J. Kripfganz, H. Perlt

Christian Brouder, Frédéric Patras

In quantum field theory (QFT), the vacuum expectation value of a normal product of creation and annihilation operators is always zero. This simple property paves the way to the classical treatment of perturbative QFT. This is no longer the case in the presence of initial correlations, that is if the vacuum is replaced by a general state. As a consequence, the combinatorics of correlated systems such as the ones occurring in many-body physics is more complex than that of quantum field theory and the general theory has made very slow progress. Similar observations hold in statistical physics or quantum probability for the perturbation series arising from the study of non Gaussian measures. In this work, an analysis of the Hopf algebraic aspects of quantum field theory is used to derive the structure of Green functions in terms of connected and one-particle irreducible Greeen functions for perturbative QFT in the presence of initial correlations.