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无序体系薛定谔算子格林函数及谱分布

陈宣玮, 阙嘉豪, 王新月   

  1. 北京师范大学数学科学学院, 北京 100875
  • 收稿日期:2020-11-12 发布日期:2021-03-18
  • 通讯作者: 阙嘉豪,Email:quejiahao@live.com.
  • 基金资助:
    国家级大学生创新创业训练计划.

陈宣玮, 阙嘉豪, 王新月. 无序体系薛定谔算子格林函数及谱分布[J]. 数值计算与计算机应用, 2021, 42(1): 56-70.

Chen Xuanwei, Que Jiahao, Wang Xinyue. GREEN'S FUNCTION AND SPECTRAL DISTRIBUTION OF SCHRODINGER OPERATOR FOR DISORDERED SYS[J]. Journal on Numerica Methods and Computer Applications, 2021, 42(1): 56-70.

GREEN'S FUNCTION AND SPECTRAL DISTRIBUTION OF SCHRODINGER OPERATOR FOR DISORDERED SYS

Chen Xuanwei, Que Jiahao, Wang Xinyue   

  1. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
  • Received:2020-11-12 Published:2021-03-18
无序体系通常有着独特的光电性质,随着材料应用的深入,无序体系渐渐引起关注.研究无序体系的物理性质,最重要的便是它的电子性质,这与薛定谔算子谱的性质有关.而研究薛定谔算子谱的性质,关键是要研究格林函数的衰减性.它从数理角度描述了微观粒子的运动状态,对相应物理现象的解释和预测很有意义.通过两类典型无序体系薛定谔算子格林函数的衰减性质及谱分布的相关推论,可以看出,两种算子具有一定相似性,但目前对这两种算子格林函数衰减性的研究采用的是不同的方法.后续可以寻求更统一的对准周期体系和随机体系或其他无序体系特征函数局域化的研究方法,并推广到更一般的无序体系中.
Disordered systems usually have unique optoelectronic properties. With the development of material application, disordered systems attracted more and more attention. The most important physical property of disordered systems is its electronic properties, which are related to the properties of the Schrödinger operator spectrum. The key to study the properties of Schrödinger operator spectrum is the attenuation of Green's function. It can describe the state of microscopic particles mathematically, and it is of great significance to explain and predict corresponding physical phenomena. According to the attenuation properties of Schrödinger operator Green's function of two typical disordered systems and related corollaries of spectral distribution, it can be seen that two operators are similar, but current research methods of these are different. In the future, we can seek more unified research methods for the localization of eigenfunctions of quasi-periodic systems, stochastic systems and other disordered systems, and extend them to more general disordered systems.

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