Singularities in spectra of disordered systems: an instanton approach for arbitrary dimension and randomness
Singularities in spectra of disordered systems: an instanton approach for arbitrary dimension and randomness
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无序系统谱中的奇点：任意维度和随机性的瞬子方法
DOI：
10.1209/0295-5075/9/5/001
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发表时间：
1989
期刊：
影响因子：
1.8
通讯作者：
J. Luck
中科院分区：
文献类型：
--
作者：
T. Nieuwenhuizen;J. Luck
随机系统的谱通常在带边缘的态密度上有一个指数奇点（Lifshitz尾）：这个奇点是一个纯指数奇点，例如，具有二元势分布的Anderson模型。最近已经证明，至少在一个维度上，利夫希茨奇点在均匀分布的情况下受到普遍对数修正的影响。利夫希茨尾的精确形式在这里通过场论描述和瞬子演算推导出来。这个非常一般的格式为任意维的任意势分布提供了新的结果。
The spectra of random systems usually have an exponential singularity (Lifshitz tail) in the density of states at band edges: this singularity is a pure exponential for, e.g., the Anderson model with a binary potential distribution. It has been shown recently, at least in one dimension, that the Lifshitz singularity is affected by a universal logarithmic correction in the case of, e.g., uniform distributions. The precise form of the Lifshitz tail is derived here, by means of a field-theoretic description, and of instanton calculus. This very general scheme provides new results for an arbitrary distribution of potentials, in arbitrary dimension.