On the role of second number-conserving functional derivatives

Abstract

It is found that number-conserving second derivatives, of functional differentiation constrained to the domain of functional variables ρ ( x ) of a given norm ∫ ρ ( x ) d x , are not obtained via two successive number-conserving differentiations, contrary to the case of unrestricted second derivatives. Investigating the role of second number-conserving derivatives, with the density-functional formulation of time-dependent quantum mechanics in focus, it is shown how number-conserving differentiation handles the dual nature of the Kohn–Sham potential arising in the practical use of the theory. On the other hand, it is pointed out that number-conserving derivatives cannot resolve the causality paradox connected with the second derivative of the exchange-correlation part of the action density functional.