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Numerical quadrature in the Brillouin zone for periodic Schrödinger operators

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1805.07144.pdf (1.618Mb)
Date
2020
Dewey
Analyse
Sujet
Schrödinger operators
Journal issue
Numerische Mathematik
Volume
144
Number
3
Publication date
01-2020
Article pages
479-526
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00211-019-01096-w
URI
https://basepub.dauphine.fr/handle/123456789/20888
Collections
  • CEREMADE : Publications
Metadata
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Author
Cancès, Éric
51621 Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
Ehrlacher, Virginie
51621 Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
Gontier, David
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Levitt, Antoine
51621 Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
Lombardi, Damiano
542019 Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Type
Article accepté pour publication ou publié
Abstract (EN)
As a consequence of Bloch’s theorem, the numerical computation of the fermionic ground state density matrices and energies of periodic Schrödinger operators involves integrals over the Brillouin zone. These integrals are difficult to compute numerically in metals due to discontinuities in the integrand. We perform an error analysis of several widely-used quadrature rules and smearing methods for Brillouin zone integration. We precisely identify the assumptions implicit in these methods and rigorously prove error bounds. Numerical results for two-dimensional periodic systems are also provided. Our results shed light on the properties of these numerical schemes, and provide guidance as to the appropriate choice of numerical parameters.

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