Lifschitz tail in a magnetic field: the nonclassical regime

• 成果类型: Article
• 署名作者: Erdos, L
• 署名单位: New York University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400050193
• 发表日期: 1998
• 页码: 321-371
• 关键词: random schrodinger-operators; wiener sausage; density; STATES; asymptotics; impurities; potentials

摘要

We obtain the Lifschitz tail, i.e. the exact low energy asymptotics of the integrated density of states (IDS) of the two-dimensional magnetic Schrodinger 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 Brezin, Gross and Itzykson 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.