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.
François Germinet 1 ; Abel Klein 2 ; Jeffrey H. Schenker 3
@article{10_4007_annals_2007_166_215,
author = {Fran\c{c}ois Germinet and Abel Klein and Jeffrey H. Schenker},
title = {Dynamical delocalization in random {Landau} {Hamiltonians}},
journal = {Annals of mathematics},
pages = {215--244},
year = {2007},
volume = {166},
number = {1},
doi = {10.4007/annals.2007.166.215},
mrnumber = {2342695},
zbl = {1159.82009},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.166.215/}
}
TY - JOUR AU - François Germinet AU - Abel Klein AU - Jeffrey H. Schenker TI - Dynamical delocalization in random Landau Hamiltonians JO - Annals of mathematics PY - 2007 SP - 215 EP - 244 VL - 166 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.166.215/ DO - 10.4007/annals.2007.166.215 LA - en ID - 10_4007_annals_2007_166_215 ER -
%0 Journal Article %A François Germinet %A Abel Klein %A Jeffrey H. Schenker %T Dynamical delocalization in random Landau Hamiltonians %J Annals of mathematics %D 2007 %P 215-244 %V 166 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.166.215/ %R 10.4007/annals.2007.166.215 %G en %F 10_4007_annals_2007_166_215
François Germinet; Abel Klein; Jeffrey H. Schenker. Dynamical delocalization in random Landau Hamiltonians. Annals of mathematics, Tome 166 (2007) no. 1, pp. 215-244. doi: 10.4007/annals.2007.166.215
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