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Pré-Publication, Document De Travail Année : 2016

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

Résumé

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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Dates et versions

hal-01271084 , version 1 (08-02-2016)
hal-01271084 , version 2 (31-03-2016)

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Raphael Ducatez. Anderson localisation for infinitely many interacting particles in Hartree-Fock theory. 2016. ⟨hal-01271084v2⟩
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