Nils Erik Dahlen

Conserving approximations in time-dependent density functional theory

In the present work, we propose a theory for obtaining successively better approximations to the linear response functions of time-dependent density or current-density functional theory. The new technique is based on the variational approach to many-body perturbation theory (MBPT) as developed during the sixties and later expanded by us in the mid-nineties. Due to this feature, the resulting response functions obey a large number of conservation laws such as particle and momentum conservation and sum rules. The quality of the obtained results is governed by the physical processes built in through MBPT but also by the choice of variational expressions. We here present several conserving response functions of different sophistication to be used in the calculation of the optical response of solids and nanoscale systems.

Time propagation of the Kadanoff-Baym equations for inhomogeneous systems

We have developed a time-propagation scheme for the Kadanoff-Baym equations for general inhomogeneous systems. These equations describe the time evolution of the nonequilibrium Green function for interacting many-body systems in the presence of time-dependent external fields. The external fields are treated nonperturbatively whereas the many-body interactions are incorporated perturbatively using Phi-derivable self-energy approximations that guarantee the satisfaction of the macroscopic conservation laws of the system. These approximations are discussed in detail for the time-dependent Hartree-Fock, the second Born, and the GW approximation.

Total energies from variational functionals of the Green function and the renormalized four-point vertex

We derive variational expressions for the grand potential or action in terms of the many-body Green function

Variational second-order Moller-Plesset theory based on the Luttinger-Ward functional

G

Propagating the Kadanoff-Baym equations for atoms and molecules

which describes the propagation of particles and the renormalized four-point vertex

Variational energy functionals tested on atoms

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Double ionization of a two-electron system in the time-dependent extended Hartree-Fock approximation

which describes the scattering of two particles in many-body systems. The main ingredient of the variational functionals is a term we denote as the

Introduction to the Keldysh formalism and applications to time-dependent density-functional theory

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Propagating the Kadanoff-Baym equations for atoms

-functional which plays a role analogously to the usual

Progress in Nonequilibrium Green's Functions III

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