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From the Keldysh Formalism to Non-equilibrium Dynamical Mean-Field Theory

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Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 191)

Abstract

Using femto-second laser-pulses one can investigate correlated electrons in solids far from equilibrium, and possibly even manipulate their behavior in a controlled and ultrafast manner. The theoretical understanding of such non-equilibrium situations meets considerable challenges, as established concepts like quasiparticles are rigorously defined only in the limit of low-energy equilibrium states. In these notes we discuss the foundations of non-equilibrium dynamical mean-field theory, an approach which allows to investigate the dynamics of correlated electron systems on microscopic timescales. We start from the definition of real-time Green’s functions, which provide a rigorous framework to interpret electronic structure out of equilibrium. We then introduce the Keldysh formalism and its relation to the description of non-equilibrium states in terms of kinetic equations. Finally we discuss non-equilibrium dynamical mean-field theory and some of its applications. We focus on photo-induced states in Mott insulators, which provides a paradigm example for a non-equilibrium system where well-defined quasiparticles are not established.

Notes

Acknowledgements

These notes are based on a series of lectures given at the XX. Training Course in the Physics of Strongly Correlated Systems. The author would like to thank Ferdinando Mancini and Roberta Citro for organizing this fruitful summer school over the years, and the participants of the training course for actively contributing to a productive and enjoyable atmosphere.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Friedrich-Alexander Universität Erlangen-NürnbergErlangenGermany

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