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Locality of the Thomas-Fermi-von Weizsäcker Equations

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Nazar, Faizan Q. and Ortner, Christoph (2016) Locality of the Thomas-Fermi-von Weizsäcker Equations. Archive for Rational Mechanics and Analysis, 224 (3). 817. doi:10.1007/s00205-017-1075-6 ISSN 0003-9527.

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Official URL: http://doi.org/10.1007/s00205-017-1075-6

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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.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Differential equations, Nonlinear -- Numerical solutions., Thomas-Fermi theory., Quantum theory., Mathematical physics.
Journal or Publication Title: Archive for Rational Mechanics and Analysis
Publisher: Springer
ISSN: 0003-9527
Official Date: June 2016
Dates:
DateEvent
June 2016Published
16 December 2016Accepted
Volume: 224
Number: 3
Article Number: 817
DOI: 10.1007/s00205-017-1075-6
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 9 January 2017
Date of first compliant Open Access: 30 March 2017
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