Locality of the Thomas-Fermi-von Weizs\"acker Equations

TL;DR

This paper proves a local stability estimate for the Thomas-Fermi-von Weizs"acker model, showing local perturbations lead to local responses in electron density and potential, with implications for energy partitioning and defect neutrality.

Contribution

It introduces a pointwise stability estimate for the TFW equations, linking local nuclear perturbations to local electronic responses, extending previous existence and uniqueness results.

Findings

Demonstrates exponential convergence rate for thermodynamic limit

Shows energy partition into exponentially localized site energies

Establishes exponential locality of forces and charge neutrality of defects

Abstract

We establish a pointwise stability estimate for the Thomas-Fermi-von Weizs\"acker (TFW) model, which demonstrates that a local perturbation of a nuclear arrangement results also in a local response in the electron density and electrostatic potential. The proof adapts the arguments for existence and uniqueness of solutions to the TFW equations in the thermodynamic limit by Catto et al. (1998). To demonstrate the utility of this combined locality and stability result we derive several consequences, including an exponential convergence rate for the thermodynamic limit, partition of total energy into exponentially localised site energies (and consequently, exponential locality of forces), and generalised and strengthened results on the charge neutrality of local defects.