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Anderson localisation for infinitely many interacting particles in Hartree-Fock theory

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Date
2018
Link to item file
https://hal.archives-ouvertes.fr/hal-01271084
Dewey
Sciences connexes (physique, astrophysique)
Sujet
multiscale analysis.; Hartree-Fock theory; Anderson localisation
Journal issue
Journal of Spectral Theory
Volume
8
Number
3
Publication date
2018
Article pages
1019-1050
Publisher
European Mathematical Society
DOI
http://dx.doi.org/10.4171/JST/221
URI
https://basepub.dauphine.fr/handle/123456789/17249
Collections
  • CEREMADE : Publications
Metadata
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Author
Ducatez, Raphaël
Type
Article accepté pour publication ou publié
Abstract (EN)
We prove the occurrence of Anderson localisation for a system of infinitely many particles interacting with a short range potential, within the ground state Hartree-Fock approximation. We assume that the particles hop on a discrete lattice and that they are submitted to an external periodic potential which creates a gap in the non-interacting one particle Hamiltonian. We also assume that the interaction is weak enough to preserve a gap. We prove that the mean-field operator has exponentially localised eigenvectors, either on its whole spectrum or at the edges of its bands, depending on the strength of the disorder.

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