Nonlinear instability of density-independent orbital-free kinetic energy functionals

TL;DR

This paper investigates the mathematical stability of certain orbital-free kinetic energy functionals, showing they are linearly stable but nonlinearly unstable, with examples of negative kinetic energy for specific densities.

Contribution

It demonstrates the nonlinear instability of a class of orbital-free kinetic energy functionals and provides explicit examples illustrating negative kinetic energy.

Findings

Models are linearly stable but nonlinearly unstable.

Kinetic energy functionals are not bounded from below.

Explicit example of negative kinetic energy density.

Abstract

We study in this article the mathematical properties of a class of orbital-free kinetic energy functionals. We prove that these models are linearly stable but nonlinearly unstable, in the sense that the corresponding kinetic energy functionals are not bounded from below. As a matter of illustration, we provide an example of an electronic density of simple shape the kinetic energy of which is negative.