2016/02/09 by Raphaël Ducatez, Ducatez, Raphael
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Quantum many-body systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1602.02896
openalex publication_date 2016/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove the occurrence of Anderson localisation for a system of infinitely\nmany particles interacting with a short range potential, within the ground\nstate Hartree-Fock approximation. We assume that the particles hop on a\ndiscrete lattice and that they are submitted to an external periodic potential\nwhich creates a gap in the non-interacting one particle Hamiltonian. We also\nassume that the interaction is weak enough to preserve a gap. We prove that the\nmean-field operator has exponentially localised eigenvectors, either on its\nwhole spectrum or at the edges of its bands, depending on the strength of the\ndisorder.\n