论文标题
Anderson本地化中的波函数极值统计
Wavefunction extreme value statistics in Anderson localization
论文作者
论文摘要
我们考虑了一个无序的一维紧密结合模型，具有幂律腐烂的跳跃幅度，以披露与安德森本地化现象相关的波函数最大分布。在扩展状态的状态下，波函数强度遵循搬运工 - 托马斯分布，而其最大值则采用牙龈分布。在临界点，不同的缩放定律控制着具有多重分子奇异性光谱的小波函数强度的机制。据报道，最大值偏离通常的牙龈形式，并报告了一些特征性的有限尺寸缩放指数。在本地化方案中，波函数强度分布已显示出一系列预先法律，幂律，指数和异常的局部策略。它们的值密切相关，这显着影响了新出现的极值分布。
We consider a disordered one-dimensional tight-binding model with power-law decaying hopping amplitudes to disclose wavefunction maximum distributions related to the Anderson localization phenomenon. Deeply in the regime of extended states, the wavefunction intensities follow the Porter-Thomas distribution while their maxima assume the Gumbel distribution. At the critical point, distinct scaling laws govern the regimes of small and large wavefunction intensities with a multifractal singularity spectrum. The distribution of maxima deviates from the usual Gumbel form and some characteristic finite-size scaling exponents are reported. Well within the localization regime, the wavefunction intensity distribution is shown to develop a sequence of pre-power-law, power-law, exponential and anomalous localized regimes. Their values are strongly correlated, which significantly affects the emerging extreme values distribution.
