Spectral Localization by Gaussian Random Potentials in Multi-Dimensional Continuous Space
Spectral Localization by Gaussian Random Potentials in Multi-Dimensional Continuous Space
复制标题
多维连续空间中高斯随机势的谱定位
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
P. Mueller
中科院分区：
文献类型：
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作者：
W. Fischer;H. Leschke;P. Mueller
给出了多维欧氏空间中非相对论量子粒子在适当随机势作用下的能谱几乎必然存在纯点分量的详细数学证明。这一结果特别适用于一类关于欧几里得平移齐次的零均值高斯随机势。更准确地说，对于这些高斯随机势，谱几乎肯定只在足够负的能量下是纯点，或者在负能量下，对于足够弱的无序。这一证明是基于固定能量多尺度分析，该分析允许不同长度尺度上的不同随机势。
A detailed mathematical proof is given that the energy spectrum of a non-relativistic quantum particle in multi-dimensional Euclidean space under the influence of suitable random potentials has almost surely a pure-point component. The result applies in particular to a certain class of zero-mean Gaussian random potentials, which are homogeneous with respect to Euclidean translations. More precisely, for these Gaussian random potentials the spectrum is almost surely only pure point at sufficiently negative energies or, at negative energies, for sufficiently weak disorder. The proof is based on a fixed-energy multi-scale analysis which allows for different random potentials on different length scales.