Far-from-equilibrium quantum many-body dynamics

A theory of real-time quantum many-body dynamics is evaluated in detail. It is based on a generating functional of correlation functions where the closed time contour extends only to a given time. Expanding the contour from this time to a later time leads to a dynamic flow of the generating functional. This flow describes the dynamics of the system and has an explicit causal structure. In the present work it is evaluated within a vertex expansion of the effective action leading to time-evolution equations for Green functions. These equations are applicable for strongly interacting systems as well as for studying the late-time behavior of non-equilibrium time evolution. For the specific case of a bosonic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{N}$\end{document}-component φ4-theory with contact interactions an s-channel truncation is identified to yield equations identical to those derived from the 2PI effective action in next-to-leading order of a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1/\mathcal{N}$\end{document} expansion. The presented approach allows to directly obtain non-perturbative dynamic equations beyond the widely used 2PI approximations.