Application of string theory to localization problem

弦理论在定位问题中的应用

• 批准号: 04452048
• 负责人: HIKAMI Shinobu
• 金额: $ 0.45万
• 依托单位: University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1992
• 资助国家: 日本
• 起止时间: 1992 至 1993
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-04452048/
• 关键词: String theory; Anderson localization; Two dimensional gravity; Matrix model; Quantum Hall effect; 弦理論; 二次元量子重力; イジング模型

Anderson localization has been studied by field theoretical method. In this research, the relation to string theory is investigated and by the use of the string scattering amplitude, the renormalization group equation for the Anderson localization is determined up to five-loop order. The multi-moment of conductivity fluctuation is also shown to be related to the dilaton and the massive field renormalizations. The string theory is closely related to the two-dimensional gravity coupled to matter fields. Matrix model for such case is investigated especially for the central charge c greater than one. The string susceptibility is evaluated from the perturbative series expansion. In a strong magnetic field, two dimensional electron within the lowest Landau level shows the quantum Hall effect. In a two-subband model, the state at the band center is shown to be delocalized and the exact value of the conductivity is obtained. Two dimensional electron in a strong magnetic field is described by Laughlin wave function. Using a complex matrix, which represents the two dimensional coordinate of electrons, we evaluate the correlation function at the edge state and confirmed the result of the conformal field theory. Also the relation to the two dimensional gravity is investigated by adding the interaction term.

用场论方法研究了安德森局域化。在这项研究中，弦理论的关系进行了调查，并通过使用弦散射振幅，重正化群方程的安德森本地化确定到五圈的顺序。电导率涨落的多矩也被证明是与介子和质量场重整化有关的。弦理论与耦合到物质场的二维引力密切相关。特别是当中心电荷c大于1时，研究了这种情况的矩阵模型。弦磁化率由微扰级数展开计算。在强磁场中，最低朗道能级的二维电子表现出量子霍尔效应。在两个子带模型中，在带中心的状态被示出为离域的电导率的精确值被获得。用Laughlin波函数描述强磁场中的二维电子。利用一个表示电子二维坐标的复矩阵，我们计算了边缘态的关联函数，证实了共形场理论的结果。并通过加入相互作用项，研究了与二维引力的关系。

项目成果

S.Hikami: "Finite N analysis of matrix models for n-Ising spin on a random surface" Physica A. (印刷中). (1994)

S. Hikami：“随机表面上 n-Ising 自旋的矩阵模型的有限 N 分析”Physica A.（出版中）。

S.Hikami and E.Brezin: "Perturbative analysis of an n-Ising model on a random surface" Physics Letters. B295. 209-213 (1992)

S.Hikami 和 E.Brezin：“随机表面上 n-Ising 模型的微扰分析”《物理快报》。

S.Hikami, M.Shirai and F.Wegner: "Anderson localization in the lowest Landau level for a two-subband model" Nuclear Physics. B408[FS]. 415-426 (1993)

S.Hikami、M.Shirai 和 F.Wegner：“双子带模型最低朗道能级的安德森定位”核物理。

S.Hikami: "Exponent of n-Ising matter fields coupled to 2d gravity" Physics Letters B. 305. 327-331 (1993)

S.Hikami：“耦合到二维引力的 n-Ising 物质场的指数”《物理快报》B. 305. 327-331 (1993)

S.Hikami: "Correlation effect in low dimensional electron system" ed.by A.Okiji,Springer-Verlag, (1994)

S.Hikami：“低维电子系统中的相关效应”，A.Okiji 编，Springer-Verlag，（1994 年）