On Mott's formula for the ac-conductivity in the Anderson model

• 成果类型: Article
• 署名作者: Klein, Abel; Lenoble, Olivier; Mueller, Peter
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2007.166.549
• 发表日期: 2007
• 页码: 549-577
• 关键词: strong localization regime; noncrystalline systems; large disorder; transport; spectrum; absence; STATES; diffusion; bounds; PROOF

摘要

We study the ac-conductivity in linear response theory in the general framework of ergodic magnetic Schrodinger operators. For the Anderson model, if the Fermi energy lies in the localization regime, we prove that the ac-conductivity is bounded from above by Cv(2)(log1/v)(d+2) at small frequencies v. This is to be compared to Mott's formula, which predicts the leading term to be Cv(2)(log1/v)(d+1).