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

Ducatez, Raphaël (2018), Anderson localisation for infinitely many interacting particles in Hartree-Fock theory, Journal of Spectral Theory, 8, 3, p. 1019-1050. 10.4171/JST/221

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01271084
Date
2018
Journal name
Journal of Spectral Theory
Volume
8
Number
3
Publisher
European Mathematical Society
Pages
1019-1050
Publication identifier
10.4171/JST/221
Metadata
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Author(s)
Ducatez, Raphaël
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.
Subjects / Keywords
multiscale analysis.; Hartree-Fock theory; Anderson localisation

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