Dynamical Localization for Discrete and Continuous Random Schrödinger Operators

Dynamical Localization for Discrete and Continuous Random Schrödinger Operators
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离散和连续随机薛定谔算子的动态定位

DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
S. Bievre
S. Bievre
中科院分区：
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文献类型：
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作者：
F. Germinet;S. Bievre

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翻译后摘要：我们显示了一个大类的随机薛定谔算子H o on和动力学本地化持有，即，概率为1，对于一个合适的能量区间I和q一个正的真实的， 这里，λ是足够快地减小的函数，并且PI（Ho）是对应于间隔I的Ho的光谱投影仪。这个结果是通过控制H_o的本征函数的衰减而得到的，在离散情况下，它覆盖了具有Bernoulli势（维数ν = 1）或奇异势（ν > 1）的安德森紧束缚模型，在连续情况下，它覆盖了安德森和随机朗道哈密顿量.
Abstract:We show for a large class of random Schrödinger operators Hο on and on that dynamical localization holds, i.e. that, with probability one, for a suitable energy interval I and for q a positive real, Here ψ is a function of sufficiently rapid decrease, and PI(Hο) is the spectral projector of Hο corresponding to the interval I. The result is obtained through the control of the decay of the eigenfunctions of Hο and covers, in the discrete case, the Anderson tight-binding model with Bernoulli potential (dimension ν = 1) or singular potential (ν > 1), and in the continuous case Anderson as well as random Landau Hamiltonians.