Effective Interaction between Electrons and Its Application to Quantum Dots

电子间的有效相互作用及其在量子点中的应用

• 批准号: 12640291
• 负责人: TAKAYANAGI Kazuo
• 金额: $ 1.92万
• 依托单位: Sophia University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640291/
• 关键词: Short Range Correlation; Effective Interaction; Nonlocal Potential; Spin Density Response; Charge Density Response; 量子ドット

First, we have developed an effective electron-electron interaction in the medium. The interaction features the short range correlations expressed by multiple scattering processes. The effective interaction is derived by using the separable approximation and the density matrix expansion to the solution of the Bethe-Goldstone equation. The obtained interaction is highly nonlocal, and consequently the p-wave interaction is important. We have expressed the effective interaction as a function of the density(r_s) and the polarization (ξ), which allows applications to various 2D electron systems.Second, we have investigated the response functions of 2D electron systems under a magnetic field in the framework of the extended RPA. Our results are in accordance with empirical findings, and stress the important roles played by the 2-particle-2-hole degrees of freedom.Third, we have studied the relation between the local and the nonlocal potential in the description of quantum many body systems. Our approach gives an intuitive insight into the effects of the nonlocality of the potential.

首先，我们在介质中建立了有效的电子-电子相互作用。这种相互作用的特征是由多次散射过程表示的短程关联。通过对Bethe-Goldstone方程的解进行可分离近似和密度矩阵展开，导出了有效相互作用。得到的相互作用是高度非局域的，因此p波相互作用是重要的。我们将有效相互作用表示为密度（r_s）和极化（r_s）的函数，这使得我们可以应用于各种二维电子系统。其次，我们在扩展的RPA框架下研究了二维电子系统在磁场作用下的响应函数。我们的结果与实验结果一致，并强调了2粒子2空穴自由度的重要作用。第三，我们研究了量子多体系统描述中定域势与非定域势的关系。我们的方法提供了一个直观的洞察力的潜在的非局部性的影响。

项目成果

D.Shindo: "Extended Random Phase Approximation in a Solvable Model"Physical Review C. 68. 014312 (2003)

D.Shindo：“可解模型中的扩展随机相位近似”物理评论 C.68.014312 (2003)

K.Yoshizawa: "Charge Density Response Function in a 2D Electron Systems under a Magnetic Field"Physical Review B. (in press). (2004)

K.Yoshizawa：“磁场下二维电子系统中的电荷密度响应函数”物理评论 B.（正在出版）。

M. Furuichi, K. Shimizu, S. Takeuchi: "Description of SU(3) Octet and Decuplet Baryons"Physical Review. C65. 025201-025207 (2002)

M. Furuichi、K. Shimizu、S. Takeuchi：“SU(3) 八重态和十重重子的描述”物理评论。

S.Takeuchi: "Pauli Blocking Effect in a Quark Cluster Model"Nuclear Physics A. 723. 408-426 (2003)

S.Takeuchi：“夸克团簇模型中的泡利阻塞效应”核物理 A. 723. 408-426 (2003)

S.Takeuchi, K.shimizu: "Quark Model and Equivalent Local Potential"Physical Review. C65. 1-10 (2002)

S.Takeuchi、K.shimizu：“夸克模型和等效局域势”物理评论。