A characterization of the Anderson metal-insulator transport transition

摘要: We investigate the Anderson metal-insulator transition for random Schrodinger operators. define strong insulator region to be part of spectrum where operator exhibits dynamical localization in Hilbert-Schmidt norm. introduce a local transport exponent β(E) and set weak metallic with nontrivial (i.e., β(E)>0). prove that these regions are complementary sets provides characterization transition. Moreover, we show if there is such transition, then has discontinuous at mobility edge. More precisely, nontrivial, β(E)≥1/(2d), d space dimension. These results follow from proof slow quantum waves media implies starting hypothesis authors' bootstrap multiscale analysis. also conclude coincides can perform analysis, proving analysis valid all way up