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Quantum Holonomy and its Application

量子完整性及其应用

基本信息

批准号：
62540216
负责人：
KURATSUJI Hiroshi
金额：
$ 0.9万
依托单位：
Ritsumeikan University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1987
资助国家：
日本
起止时间：
1987 至 1988
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-62540216/
关键词：
adiabatic phase level crossing gauge field chiral anomaly supersymmetry mean field BCS model Mott insulator fractional statistics guantum Hall effect 超流動量子ホール効果正準位相断熱変形 WKB 超対称ヤーンテラー効果

项目摘要

We have obtained the following results on the specific features of the quantum adiabatic phase.(1): A quantitative estimate of the effect of the adiabatic phase has been carried out for the rotational-particle coupling model of nuclei.(2): Concerning the connection between the adiabatic phase and the chiral anomaly in non-abelian gauge field, the anomalous commutators for the generators of gauge transformation is formulated as the deformation of the symplectic structure associated with the gauge field.(3): The supersymmetric (SUSY) quantum mechanics has been obtained as a remarkable consequence of the WKP theory including the adiabatic phase.(4): As applications of the adiabatic phase to condensed matter physics, we have examined the effect on the mean field theory of many-particle models. Among others, (i) the BCS superconductivity model, for which we deduce that the charge of the cooper pair becomes fractional. (ii) the Mott insulator, for which the quantum number carried by the mode of order parameter describing the particlehole condensate becomes fractional as an effect of the adiabatic phase.(5): The topological quantization of the transport coefficient in superfluid He^3 is conjectured as an effect of the phase holonomy accompany in the adiabatic change of the order parameter phase, which can be regarded as a direct analogy with the quantum Hall effect.(6): The concept of "canonical phase" is formulated as a generalization of the adiabatic phase by using the generalized coherent state.

关于量子绝热相的特殊性质，我们得到了下列结果。(1)本文对核的转动-粒子耦合模型中绝热相的影响作了定量估计。(2)关于非阿贝尔规范场的绝热相与手征反常之间的联系，规范变换生成元的反常子被表述为与规范场相关联的辛结构的变形。(3)：超对称（SUSY）量子力学是作为包括绝热相的WKP理论的显着结果而获得的。(4)作为绝热相在凝聚态物理中的应用，我们考察了绝热相对多粒子模型平均场理论的影响。其中，（i）BCS超导模型，我们推导出库珀对的电荷变成分数。(ii)Mott绝缘体，对于这种绝缘体，描述粒子空穴凝聚的序参量模所携带的量子数由于绝热相的影响而变成分数。(5)超流He^3中输运系数的拓扑量子化被证明是序参量相的绝热变化所伴随的相完整性效应，它可以被看作是量子霍尔效应的直接类比。(6)利用广义相干态，将绝热相的概念推广为“正则相”的概念。