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

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 classification 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 classification of the non-uniqueness of the non-local potential in 1RDM functional theory can be given for the first time.

11 pages, 1 figure

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Cited by in corpus (5)

• Thermal density functional theory: Time-dependent linear response and approximate functionals from the fluctuation-dissipation theorem
• One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures
• Deriving density-matrix functionals for excited states
• Adaptive cluster approximation for reduced density-matrix functional theory
• Invertibility of the retarded response functions for initial mixed states: application to one-body reduced density matrix functional theory