Uncertainties of clock and shift operators for an electron in one-dimensional nonuniform lattice systems

doi:10.1088/1674-1056/26/11/117201

中国物理B ›› 2017, Vol. 26 ›› Issue (11): 117201-117201.doi: 10.1088/1674-1056/26/11/117201

• CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES • 上一篇下一篇

Uncertainties of clock and shift operators for an electron in one-dimensional nonuniform lattice systems

Long-Yan Gong(巩龙延), You-Gen Ding(丁友根), Yong-Qiang Deng(邓永强)

1. Department of Applied Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;
2. Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;
3. National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China

收稿日期:2017-06-02 修回日期:2017-07-30 出版日期:2017-11-05 发布日期:2017-11-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61475075 and 61170321).

Uncertainties of clock and shift operators for an electron in one-dimensional nonuniform lattice systems

Long-Yan Gong(巩龙延)^1,2,3, You-Gen Ding(丁友根)², Yong-Qiang Deng(邓永强)²

1. Department of Applied Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;
2. Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;
3. National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China

Received:2017-06-02 Revised:2017-07-30 Online:2017-11-05 Published:2017-11-05
Contact: Long-Yan Gong E-mail:lygong@njupt.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61475075 and 61170321).

摘要/Abstract

摘要： The clock operator U and shift operator V are higher-dimensional Pauli operators. Just recently, tighter uncertainty relations with respect to U and V were derived, and we apply them to study the electron localization properties in several typical one-dimensional nonuniform lattice systems. We find that uncertainties △ U² are less than, equal to, and greater than uncertainties △ V² for extended, critical, and localized states, respectively. The lower bound LB of the uncertainty relation is relatively large for extended states and small for localized states. Therefore, in combination with traditional quantities, for instance inverse participation ratio, these quantities can be as novel indexes to reflect Anderson localization.

关键词: uncertainties, Anderson localization, nonuniform lattice systems, mobility edge

Abstract: The clock operator U and shift operator V are higher-dimensional Pauli operators. Just recently, tighter uncertainty relations with respect to U and V were derived, and we apply them to study the electron localization properties in several typical one-dimensional nonuniform lattice systems. We find that uncertainties △ U² are less than, equal to, and greater than uncertainties △ V² for extended, critical, and localized states, respectively. The lower bound LB of the uncertainty relation is relatively large for extended states and small for localized states. Therefore, in combination with traditional quantities, for instance inverse participation ratio, these quantities can be as novel indexes to reflect Anderson localization.

Key words: uncertainties, Anderson localization, nonuniform lattice systems, mobility edge

中图分类号: (Mobility edges; hopping transport)

72.20.Ee

72.15.Rn (Localization effects (Anderson or weak localization)) 71.23.An (Theories and models; localized states)

巩龙延, 丁友根, 邓永强. Uncertainties of clock and shift operators for an electron in one-dimensional nonuniform lattice systems[J]. 中国物理B, 2017, 26(11): 117201-117201.

Long-Yan Gong(巩龙延), You-Gen Ding(丁友根), Yong-Qiang Deng(邓永强). Uncertainties of clock and shift operators for an electron in one-dimensional nonuniform lattice systems[J]. Chin. Phys. B, 2017, 26(11): 117201-117201.

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Uncertainties of clock and shift operators for an electron in one-dimensional nonuniform lattice systems

Uncertainties of clock and shift operators for an electron in one-dimensional nonuniform lattice systems

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