an:01233914
Zbl 0921.60099
Erdős, László
Lifschitz tail in a magnetic field: The nonclassical regime
EN
Probab. Theory Relat. Fields 112, No. 3, 321-371 (1998).
0178-8051 1432-2064
1998
j
60K40 82B44 82D30
enlargement of obstacles method; exact low energy asymptotics; magnetic Schrödinger operator; magnetic localization techniques
Summary: We obtain the Lifschitz tail, i.e. the exact low energy asymptotics of the integrated density of states (IDS) of the two-dimensional magnetic Schrödinger operator with a uniform magnetic field and random Poissonian impurities. The single site potential is repulsive and it has a finite but nonzero range. We show that the IDS is a continuous function of the energy at the bottom of the spectrum. This result complements the earlier (nonrigorous) calculations by \textit{E. Brézin}, \textit{D. J. Gross} and \textit{C. Itzykson} [Nucl. Phys. B 235, 24-44 (1984)] which predict that the IDS is discontinuous at the bottom of the spectrum for zero range (Dirac delta) impurities at low density. We also elucidate the reason behind this apparent controversy. Our methods involve magnetic localization techniques (both in space and energy) in addition to a modified version of the ``enlargement of obstacles'' method developed by A.-S. Sznitman.