Anderson Localization for a Class of Models with a Sign-Indefinite Single-Site Potential via Fractional Moment Method
Anderson Localization for a Class of Models with a Sign-Indefinite Single-Site Potential via Fractional Moment Method
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基于分数矩法的一类符号不定单点势模型的安德森定位
DOI：
10.1007/s00023-011-0112-5
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
I. Veselić
中科院分区：
文献类型：
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作者：
A. Elgart;Martin Tautenhahn;I. Veselić
Anderson局部化的一个技术上方便的特征是格林函数的分数阶矩在适当的能量范围内指数衰减。我们考虑格上的随机哈密顿量，它的随机性是由符号不定的单位点势产生的，但在其支集的边界上是符号定的。对于这类Anderson算子，我们建立了一个有限体积准则，它意味着分数阶矩衰减性质成立。这一构造性判据在典型的微扰区域满足，例如在满足Lifshitz尾部估计的态密度和足够强的无序的谱边界上满足。我们还展示了分数阶矩方法如何方便地证明这种随机势的指数(谱)局部化。
A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated by the sign-indefinite single-site potential, which is however sign-definite at the boundary of its support. For this class of Anderson operators, we establish a finite-volume criterion which implies that the fractional moment decay property holds. This constructive criterion is satisfied at typical perturbative regimes, e.g. at spectral boundaries which satisfy “Lifshitz tail estimates” on the density of states and for sufficiently strong disorder. We also show how the fractional moment method facilitates the proof of exponential (spectral) localization for such random potentials.