Operator-Theoretical Research of Two-Body System in Non-Relativistic Quantum Field Theory

非相对论量子场论中二体系统算子理论研究

基本信息

批准号：
18540180
负责人：
HIROKAWA Masao
金额：
$ 2.57万
依托单位：
Okayama University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2006
资助国家：
日本
起止时间：
2006 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18540180/
关键词：
bipolaron non-relativistic nuantum field theory Nelson model phonon two-body system ground state binding energy operator theory ポーラロン場の量子論

项目摘要

We have studied the two-body system in non-relativistic quantum field theory in the light of operator theory. In particular we have been interested in the problem when the so-called bipolaron forms.Let us consider two electrons coupled with longitudinal optical (LO) phonons in a 3-dimensional crystal now. Then, in general, an electron is dressed in a phonon cloud because of the electron-phonon interaction. The dressed electron is the so-called polaron. If the Coulomb repulsion between the two electrons is strong enough, the two electrons are so far away from each other that each electron dresses itself in an individual phonon cloud. Thus, there is no exchange of phonons between the two. On the other hand, if the distance between the two electrons is so short that a common phonon cloud grasps both electrons, then the phonon-exchange takes place. In this case, there is a possibility that attraction appears between them and thus we can expect that they are bound to each other. The bound two polarons is called a bipolaron. We have explored tug of war between the two electrons. We have clarified some mathematical aspects for the bipolaron problem.

我们根据算子理论研究了非相对论量子场论中的二体系统。我们特别对所谓的双极子形成时的问题感兴趣。现在让我们考虑在 3 维晶体中与纵向光学 (LO) 声子耦合的两个电子。然后，一般来说，由于电子-声子相互作用，电子被包裹在声子云中。修饰后的电子就是所谓的极化子。如果两个电子之间的库仑斥力足够强，则两个电子彼此相距很远，以至于每个电子都会将自己包裹在一个单独的声子云中。因此，两者之间不存在声子交换。另一方面，如果两个电子之间的距离很短，以至于公共声子云抓住了两个电子，那么就会发生声子交换。在这种情况下，它们之间有可能出现吸引力，因此我们可以预期它们彼此绑定。结合的两个极化子称为双极化子。我们已经探索了两个电子之间的拉锯战。我们已经阐明了双极子问题的一些数学方面。