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Analysis on Superlattices using Spectral Analysis of Pauli Operator

利用泡利算子谱分析进行超晶格分析

基本信息

批准号：
17540191
负责人：
OGURISU Osamu
金额：
$ 1.8万
依托单位：
Kanazawa University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2007
项目状态：
已结题

项目摘要

Energy filters based on superlattices are a kind of semi-conductor devices using quantum effects. In our study, we investigate this superlattice structure as a mathematical object with considering requirements from the point of industrial view, that is, we want to decide the potential to gain the desired transmission probability. This is an inverse scattering problem on one-dimensional Schroedinger operators. We obtained the following results with the aid of M. Suzuki, H. Sanada and K Asakura.1 We show that Gaussian superlattice modulated layer thickness and one with delta interaction potential form a band structure, which consists of real pass bands, quasi pass bands and stop bands. We propose a method to estimate the real pass bands using image parameters.2 We propose a new kind of effective potential of modulated superlattices. This new potential make us to explain the reason why quasi pass bands appear, that is, the resonances for the double wall structure of the new potential make them.3 We give a sufficient condition for a one-dimensional Schroedinger operator with point delta interactions, which contain m points of interaction with negative intensities, to have at least m negative eigenvalues. This model contains superlattices as special cases.4 We obtain a new functional form of the Green's function of discrete Laplacian L on Z. The new form is a composition of elementary functions (sin, arccos and exponential functions). Using this, we can investigate the spectral properties of L more easily.

基于超晶格的能量滤光片是一种利用量子效应的半导体器件。在我们的研究中，我们将这种超晶格结构作为一个数学对象来研究，并从工业的角度考虑要求，即我们想要确定获得期望的传输几率的势。这是一个关于一维薛定谔算子的逆散射问题。借助于M.Suzuki，H.Sanada和K Asakura，我们得到了如下结果：1我们发现，具有Delta相互作用势的Gauss超晶格调制层厚度形成了一个由实通带、准通带和阻带组成的能带结构。我们提出了一种利用图像参数来估计真实通带的方法。2.我们提出了一种新的调制超晶格有效势。这个新的势使得我们能够解释为什么会出现准通带，即新的势的双壁结构的共振使得它们出现。3我们给出了一个含有m个负强度的相互作用点的一维点-Delta相互作用的薛定谔算符至少有m个负本征值的充分条件。4我们得到了离散拉普拉斯L在Z上的格林函数的一种新的泛函形式，这种新形式是初等函数(正弦函数、圆弧函数和指数函数)的组合。利用这一点，我们可以更容易地研究L的光谱性质。