2014/06/30 by John Z. Imbrie · 23 citations
Mathematics · Physics and Astronomy · #Anderson impurity model #Anderson localization #Cold Atom Physics and Bose-Einstein Condensates #Eigenfunction #Exponential function #Hamiltonian (control theory) #Matrix (chemical analysis) #Quantum #Quantum many-body systems #Sequence (biology) #Spectral Theory in Mathematical Physics #cond-mat.dis-nn #math-ph #math.MP #math.PR #msc:60K35 #msc:82B44 #msc:82D30
paper · pdf · doi:10.1007/s00220-015-2522-6
published in Communications in Mathematical Physics 341(2), 491-521 (Springer Science+Business Media) · 34 pages, 8 figures, clarifications and corrections for published version; more detail in Section 4.5
arxiv created 2015/09/30 · openalex publication_date 2015/11/30 · arxiv updated 2016/01/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A new KAM-style proof of Anderson localization is obtained. A sequence of local rotations is defined, such that off-diagonal matrix elements of the Hamiltonian are driven rapidly to zero. This leads to the first proof via multi-scale analysis of exponential decay of the eigenfunction correlator (this implies strong dynamical localization). The method has been used in recent work on many-body localization [arXiv:1403.7837].