Quantum Continuum Mechanics Made Simple

TL;DR

This paper simplifies quantum continuum mechanics by focusing on practical implementations using Kohn-Sham approximations, proving its exactness for one-electron systems, and demonstrating its application on an example system.

Contribution

It introduces a simplified, practical approach to quantum continuum mechanics, including a proof of exactness for one-electron systems and an application example.

Findings

Proved CM is exact for one-electron systems.

Developed a Kohn-Sham based approximation for CM.

Demonstrated the simplified CM on an example system.

Abstract

In this paper we further explore and develop the quantum continuum mechanics (CM) of [Tao \emph{et al}, PRL{\bf 103},086401] with the aim of making it simpler to use in practice. Our simplifications relate to the non-interacting part of the CM equations, and primarily refer to practical implementations in which the groundstate stress tensor is approximated by its Kohn-Sham version. We use the simplified approach to directly prove the exactness of CM for one-electron systems via an orthonormal formulation. This proof sheds light on certain physical considerations contained in the CM theory and their implication on CM-based approximations. The one-electron proof then motivates an approximation to the CM (exact under certain conditions) expanded on the wavefunctions of the Kohn-Sham (KS) equations. Particular attention is paid to the relationships between transitions from occupied to unoccupied KS orbitals and their approximations under the CM. We also demonstrate the simplified CM semi-analytically on an example system.