Nonequilibrium dynamics of the many-body electronic excitations in atomic, molecular and model systems

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In recent years the emergence of attosecond physics, molecular electronics and tunneling spectroscopy with atomic resolution have called for the development of new theoretical methods in condensed matter and quantum chemistry. Attosecond resolution enables one to probe electronic excitations in atomic systems and in condensed matter far from equilibrium. The time scales in molecular electronics and time resolved scanning tunneling spectroscopy are much slower. However, the systems are put in the nonequilibrium regime by the externally applied voltage. In both cases the conventional many-body perturbation theory (MBPT) ceased to be valid. The hierarchy of density matrix methods, time-dependent density functional theory (TDDFT), density matrix renormalization group (tDMRG), and the nonequilibrium Green's function (NEGF) approaches are theoretical methods capable to deal with this kind of experimental conditions.Our theoretical project will focus on the NEGF class of methods to describe the dynamics of electronic excitations in atomic, molecular and model systems far from equilibrium. The choice of the method is not arbitrary: i) In comparison with the density matrix method it is easier to find approximations which fulfill macroscopic conservation laws; ii) It is possible to consistently describe both neutral and charged excitations within a single-shot calculation; iii) The method can be used as a starting point for development exchange-correlation functionals via the Sham-Schlüter equation or optimized effective potential (OEP) approach; iv) In comparison to tDMFT the method is not limited to model systems.The NEGF methodology transformed from the pure academic tool into the powerful numerical method after Kwong and Bonitz numerically found the two-time correlation functions of the homogeneous electron gas (HEG) by propagating the Kadanoff-Baym equations, and Dahlen and van Leeuwen solved for the first time these equations for the atomic and molecular systems. While a lot of efforts have been put on testing various approximations for model systems applications of the method to realistic systems are scarce. The goal of this project is to push these methods towards a practical ab initio tool to model strongly nonequilibrium dynamics in atomic, molecular and model systems. We plan to use it to study light-matter interaction on the attosecond timescale and electron transport on the nanoscale.