Communications in Mathematical Physics Finite-Volume Fractional-Moment Criteria for Anderson Localization
Communications in Mathematical Physics Finite-Volume Fractional-Moment Criteria for Anderson Localization
复制标题
数学物理通信安德森定位的有限体积分数矩准则
DOI：
10.1016/s1385-7258(51)50054-9
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发表时间：
2001
影响因子：
0.6
通讯作者：
D. Hundertmark
中科院分区：
文献类型：
--
作者：
M. Aizenman;J. Schenker;R. Friedrich;D. Hundertmark
一个技术上方便的签名本地化，表现出离散运营商与随机潜力，是指数衰减的分数阶矩的绿色功能在适当的能量范围内。已知的影响包括：光谱局域化，没有水平排斥，强形式的动力学局域化，以及相关的条件，其中发挥了重要作用的量子化霍尔电导在二维费米气体。我们提出了一个家庭的有限体积的标准，在一些温和的限制下的潜在的分布，覆盖制度的分数矩衰减条件。建设性的标准允许建立在谱带边缘的条件下，有足够的“Lifshitz尾估计”的状态密度。他们也被用来在这里得出结论，分数矩条件，从而本地化的其他表现形式，是有效的整个政权所涵盖的“多尺度分析”。在匡威的方向上，分析排除了快速幂律衰减的绿色功能的迁移率边缘。
A technically convenient signature of localization, exhibited by discrete operators with random potentials, is exponential decay of the fractional moments of the Green function within the appropriate energy ranges. Known implications include: spectral localization, absence of level repulsion, strong form of dynamical localization, and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. We present a family of finite-volume criteria which, under some mild restrictions on the distribution of the potential, cover the regime where the fractional moment decay condition holds. The constructive criteria permit to establish this condition at spectral band edges, provided there are sufficient “Lifshitz tail estimates” on the density of states. They are also used here to conclude that the fractional moment condition, and thus the other manifestations of localization, are valid throughout the regime covered by the “multiscale analysis”. In the converse direction, the analysis rules out fast power-law decay of the Green functions at mobility edges.