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.

基于超晶格的能量过滤器是一种使用量子效应的半导体设备。在我们的研究中，我们将这种超晶格结构作为数学对象研究，从工业角度考虑要求，也就是说，我们希望确定获得所需的传输概率的潜力。这是一维Schroedinger操作员的反向散射问题。我们借助于铃木M. sanada和k asakura获得了以下结果。1我们表明高斯超级晶格调制层厚度，并且具有Delta相互作用电势形成一个带结构，其中由真实的Pass带，Quasi Pass带和停止频段组成。我们提出了一种使用图像参数估算真实通行带的方法。2我们提出了一种新型的调制超晶格的有效潜力。这种新的潜力使我们解释了出现准通道的原因，也就是说，新电位的双层壁结构的共鸣使它们产生的共鸣。3我们为一维的Schroedinger运算符提供了足够的条件，具有点数Delta相互作用，该点具有点数Delta相互作用，该点具有与负强度的M点相互作用，至少具有M负eigenvalue。该模型包含作为特殊情况的超晶格。4我们在z上获得了绿色laplacian l的绿色功能的新功能形式。新形式是基本函数（SIN，ARCCOS和指数函数）的组成。使用此过程，我们可以更轻松地研究L的光谱特性。