Skip to main content

Resonant delocalization for random Schrodinger operators on tree graphs

Author(s): Aizenman, Michael; Warzel, Simone

Download
To refer to this page use: http://arks.princeton.edu/ark:/88435/pr1nf06
Full metadata record
DC FieldValueLanguage
dc.contributor.authorAizenman, Michael-
dc.contributor.authorWarzel, Simone-
dc.date.accessioned2019-05-30T15:59:43Z-
dc.date.available2019-05-30T15:59:43Z-
dc.date.issued2013en_US
dc.identifier.citationAizenman, Michael, Warzel, Simone. (2013). Resonant delocalization for random Schrodinger operators on tree graphs. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 15 (1167 - 1222. doi:10.4171/JEMS/389en_US
dc.identifier.issn1435-9855-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1nf06-
dc.description.abstractWe analyse the spectral phase diagram of Schrodinger operators T + lambda V on regular tree graphs, with T the graph adjacency operator and V a random potential given by iid random variables. The main result is a criterion for the emergence of absolutely continuous (ac) spectrum due to fluctuation-enabled resonances between distant sites. Using it we prove that for unbounded random potentials ac spectrum appears at arbitrarily weak disorder (lambda << 1) in an energy regime which extends beyond the spectrum of T. Incorporating considerations of the Green function’s large deviations we obtain an extension of the criterion which indicates that, under a yet unproven regularity condition of the large deviations’ ‘free energy function’, the regime of pure ac spectrum is complementary to that of previously proven localization. For bounded potentials we disprove the existence at weak disorder of a mobility edge beyond which the spectrum is localized.en_US
dc.format.extent1167 - 1222en_US
dc.language.isoen_USen_US
dc.relation.ispartofJOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETYen_US
dc.rightsAuthor's manuscripten_US
dc.titleResonant delocalization for random Schrodinger operators on tree graphsen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.4171/JEMS/389-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

Files in This Item:
File Description SizeFormat 
1104.0969v3.pdf1.11 MBAdobe PDFView/Download


Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.