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

• 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

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.

我们根据操作者理论研究了非相关量子场理论中的两体系统。特别是，当我们在所谓的双极形式时，我们一直对这个问题感兴趣。然后，通常，由于电子 - 声子的相互作用，电子都穿着声子云。穿着的电子是所谓的二极星。如果两个电子之间的库仑排斥力足够强，那么两个电子彼此之间距离很远，以至于每个电子都会在单个声子云中打扮自己。因此，两者之间没有声子交换。另一方面，如果两个电子之间的距离太短，以至于共同的声子云都抓住了两个电子，则会发生声子交换。在这种情况下，它们之间存在吸引力，因此我们可以期望它们彼此绑定。绑定的两个极性子称为双极。我们已经探索了两个电子之间的战争。我们已经阐明了双极问题的一些数学方面。

项目成果

Stability of Formation of Large Bipolaron

大型双极子形成的稳定性

• 发表时间: 2007
• 期刊: 数理解析研究所講究録 1565
• 作者: Sakuma;Makoto(他3名);A. Arai;M. Hirokawa
• 通讯作者: M. Hirokawa

Regularities of ground states of quantum field models

量子场模型基态规律

• 发表时间: 2007
• 期刊: Kyushu Journal of Mathematics 61
• 作者: A. Arai;M. Hirokawa;F. Hiroshima
• 通讯作者: F. Hiroshima