Conserving Approximations in Time-Dependent Density Functional Theory

Abstract

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 nano-scale systems.

11 pages, 4 figures, revised version

References in corpus (7)

• Excitonic effects in solids described by time-dependent density functional theory
• Bound excitons in time-dependent density-functional-theory: optical and energy-loss spectra
• Many-body perturbation theory using the density-functional concept: beyond the GW approximation
• Excitonic optical spectrum of semiconductors obtained by time-dependent density-functional theory with the exact-exchange kernel
• Nonuniqueness and derivative discontinuities in density-functional theories for current-carrying and superconducting systems
• Many-body diagrammatic expansion in a Kohn-Sham basis: implications for Time-Dependent Density Functional Theory of excited states
• Introduction to the Keldysh formalism and applications to time-dependent density-functional theory

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