Archive for Rational Mechanics and Analysis

, Volume 224, Issue 3, pp 817–870

Locality of the Thomas–Fermi–von Weizsäcker Equations

Open Access

DOI: 10.1007/s00205-017-1075-6

Cite this article as:
Nazar, F.Q. & Ortner, C. Arch Rational Mech Anal (2017) 224: 817. doi:10.1007/s00205-017-1075-6


We establish a pointwise stability estimate for the Thomas–Fermi–von Weiz-säcker (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. (The mathematical theory of thermodynamic limits: Thomas–Fermi type models. Oxford mathematical monographs. The Clarendon Press, Oxford University Press, New York, 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.

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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Mathematics InstituteZeeman Building, University of WarwickCoventryUK

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