On the Integrated Density of States for Schrödinger Operators on ℤ2 with Quasi Periodic Potential
On the Integrated Density of States for Schrödinger Operators on ℤ2 with Quasi Periodic Potential
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ℤ2 准周期势薛定谔算子的态积分密度
DOI：
10.1007/pl00005584
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发表时间：
2001
影响因子：
2.4
通讯作者：
W. Schlag
中科院分区：
文献类型：
--
作者：
W. Schlag
摘要：在本文中，我们考虑具有准周期势的晶格 ℤ2 上的离散薛定谔算子。我们为积分态密度建立了新的规律性结果，以及克雷格和西蒙之前考虑的“Thouless 公式”的定量版本，用于真实能量和收敛率。主要成分是最近由 Bourgain、Goldstein 和作者建立的格林函数大偏差定理。对于积分态密度，使用布尔干论证。最后，我们建立了可能具有独立兴趣的两个变量的单独分调和函数的某些精细属性。
Abstract: In this paper we consider discrete Schrödinger operators on the lattice ℤ2 with quasi periodic potential. We establish new regularity results for the integrated density of states, as well as a quantitative version of a “Thouless formula”, as previously considered by Craig and Simon, for real energies and with rates of convergence. The main ingredient is a large deviation theorem for the Green's function that was recently established by Bourgain, Goldstein, and the author. For the integrated density of states an argument of Bourgain is used. Finally, we establish certain fine properties of separately subharmonic functions of two variables that might be of independent interest.