Invertibility of retarded response functions for Laplace transformable potentials: Application to one-body reduced density matrix functional theory

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Abstract

A theorem for the invertibility of arbitrary response functions is presented under the following conditions: the time dependence of the potentials should be Laplace transformable and the initial state should be a ground state, though it might be degenerate. This theorem provides a rigorous foundation for all density-functional-like theories in the time-dependent linear response regime. Especially for time-dependent one-body reduced density matrix (1RDM) functional theory, this is an important step forward, since a solid foundation has currently been lacking. The theorem is equally valid for static response functions in the non-degenerate case, so can be used to characterize the uniqueness of the potential in the ground state version of the corresponding density-functional-like theory. Such a classi cation of the uniqueness of the non-local potential in ground state 1RDM functional theory has been lacking for decades. With the aid of presented invertibility theorem presented here, a complete classi cation of the non-uniqueness of the non-local potential in 1RDM functional theory can be givenforthe rsttime
Original languageEnglish
Article number054102
Pages (from-to)1-9
Number of pages9
JournalJournal of Chemical Physics
Volume143
Issue number5
DOIs
Publication statusPublished - Aug 2015

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