• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail - Request a copy

Spectral Pollution and How to Avoid It (With Applications to Dirac and Periodic Schrödinger Operators)

Lewin, Mathieu; Séré, Eric (2009), Spectral Pollution and How to Avoid It (With Applications to Dirac and Periodic Schrödinger Operators), Proceedings of the London Mathematical Society, 100, 3, p. 864-900. http://dx.doi.org/10.1112/plms/pdp046

Type
Article accepté pour publication ou publié
Date
2009
Journal name
Proceedings of the London Mathematical Society
Volume
100
Number
3
Publisher
London Mathematical Society
Pages
864-900
Publication identifier
http://dx.doi.org/10.1112/plms/pdp046
Metadata
Show full item record
Author(s)
Lewin, Mathieu cc
Séré, Eric
Abstract (EN)
This paper, devoted to the study of spectral pollution, contains both abstract results and applications to some self-adjoint operators with a gap in their essential spectrum occuring in Quantum Mechanics. First we consider Galerkin basis which respect the decomposition of the ambient Hilbert space into a direct sum $H=PH\oplus(1-P)H$, given by a fixed orthogonal projector $P$, and we localize the polluted spectrum exactly. This is followed by applications to periodic Schrödinger operators (pollution is absent in a Wannier-type basis), and to Dirac operator (several natural decompositions are considered). In the second part, we add the constraint that within the Galerkin basis there is a certain relation between vectors in $PH$ and vectors in $(1-P)H$. Abstract results are proved and applied to several practical methods like the famous "kinetic balance" of relativistic Quantum Mechanics.
Subjects / Keywords
variational collapse; periodic Schrödinger operators; Wannier functions; Dirac operator; kinetic balance method; spectral pollution; spurious eigenvalues

Related items

Showing items related by title and author.

  • Thumbnail
    Spurious Modes in Dirac Calculations and How to Avoid Them 
    Séré, Eric; Lewin, Mathieu (2013) Chapitre d'ouvrage
  • Thumbnail
    Dirac-Coulomb operators with general charge distribution I. Distinguished extension and min-max formulas 
    Esteban, Maria J.; Lewin, Mathieu; Séré, Eric (2021) Article accepté pour publication ou publié
  • Thumbnail
    Distinguished self-adjoint extension and eigenvalues of operators with gaps. Application to Dirac-Coulomb operators 
    Dolbeault, Jean; Esteban, Maria J.; Séré, Eric (2022) Document de travail / Working paper
  • Thumbnail
    Dirac-Coulomb operators with general charge distribution. II. The lowest eigenvalue 
    Esteban, Maria J.; Lewin, Mathieu; Séré, Eric (2021) Article accepté pour publication ou publié
  • Thumbnail
    Corrigendum to: “On the eigenvalues of operators with gaps. Application to Dirac operators” [J. Funct. Anal. 174 (1) (2000) 208–226] 
    Dolbeault, Jean; Esteban, Maria J.; Séré, Eric (2023) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo