Holder continuity of the integrated density of states for quasi-periodic Schrodinger equations and averages of shifts of subharmonic functions
作者： Michael Goldstein , Wilhelm Schlag
DOI: 10.2307/3062114
关键词: Continued fraction 、 Mathematical analysis 、 Almost Mathieu operator 、 Monodromy 、 Monodromy matrix 、 Modulus of continuity 、 Lyapunov exponent 、 Mathematics 、 Quasiperiodic function 、 Hölder condition
摘要: In this paper we consider various regularity results for discrete quasiperiodic Schr6dinger equations --n+l - Pn-1 + V(9 nw)on = EOn with analytic potential V. We prove that on intervals of positivity the Lyapunov exponent integrated density states is Holder continuous in energy provided w has a typical continued fraction expansion. The proof based certain sharp large deviation theorems norms monodromy matrices and "avalanche-principle". latter refers to mechanism allows us write norm matrix as product many short blocks. multi-frequency case shown have modulus continuity form exp(- log tl) some 0 < 1, but currently do not obtain more than one frequency. also present proving disorders general class equations. only requirement approach weak theorem exponents. particular, an independent Herman-Sorets-Spencer case. related recent nonperturbative Anderson localization quasi-periodic by J. Bourgain M. Goldstein.
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