Dynamical delocalization in random Landau Hamiltonians

• 成果类型: Article
• 署名作者: Germinet, Francois; Klein, Abel; Schenker, Jeffrey H.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2007.166.215
• 发表日期: 2007
• 页码: 215-244
• 关键词: density-of-states; magnetic schrodinger-operators; quantized hall conductance; anderson model; classical waves; multiscale analysis; general framework; random potentials; charge-transport; extended states

摘要

We prove the existence of dynamical delocalization for random Landau Hamiltonians near each Landau level. Since typically there is dynamical localization at the edges of each disordered-broadened Landau band, this implies the existence of at least one dynamical mobility edge at each Landau band, namely a boundary point between the localization and delocalization regimes, which we prove to converge to the corresponding Landau level as either the magnetic field goes to infinity or the disorder goes to zero.