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Characterization of spectrum and eigenvectors of the Schr?dinger operator with chaotic potentials

机译:具有混沌势的薛定er算子的谱和特征向量的表征

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Chaotic sequences are sequences generated by chaotic maps. A particle moving in a one-dimensional space has its behavior modeled according to the time-independent Schr?dinger equation. The tight-binding approximation enables the use of chaotic sequences as the simulation of quantum potentials in the discretized version of the Schr?dinger equation. The present work consists of the generation and characterization of spectral curves and eigenvectors of the Schr?dinger operator with potentials generated by chaotic sequences, as well as their comparison with the curves generated by periodic, almost periodic and random sequences. This comparison is made by calculating in each case the inverse participation ratio as a function of the system size.
机译:混沌序列是由混沌图生成的序列。在一维空间中运动的粒子的行为是根据与时间无关的薛定er方程建模的。紧密绑定的近似值使得能够使用混沌序列作为Schr?dinger方程离散化版本中量子势的模拟。目前的工作包括具有混沌序列产生的电势的薛定er算子的光谱曲线和特征向量的生成和表征,以及它们与由周期性,几乎周期性和随机序列生成的曲线的比较。通过在每种情况下计算反参与率作为系统大小的函数来进行比较。

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