论文总字数：31064字

摘 要

我们首先研究了三量子位海森堡XX模型的对热纠缠，得到对热纠缠的解析表达式以及相干性的解析表达式。我们发现海森堡XX模型的对热纠缠和相干性有着明显的区别，在某个特定的条件下（x=J/Tlt;-0.7866）不存在对热纠缠，而相干性只有在x=0时不存在。其次在XX模型的基础上讨论各向异性海森堡XXZ模型的对热纠缠和量子相干，发现当各向异性参数时，无论是反铁磁性的还是铁磁性的XXZ模型，对热纠缠都不存在，但相干性仍然存在，且其数值随而变化。最后，我们讨论了均匀外磁场中的海森堡XXZ模型，研究了对热纠缠和相干性随外磁场B和交换常数J的变化，我们发现均匀磁场可以引起反铁磁系统的对热纠缠，但不能引起铁磁系统的对热纠缠，而磁场可以加强反铁磁系统的相干性，但会减弱铁磁系统的相干性。

关键词：三量子位 海森堡模型 对热纠缠 相干性

Abstract

We study pairwise thermal entanglement in three-qubit Heisenberg models primarily and obtain analytic expressions of concurrence and coherence.We find that the concurrence is obviously different from correlation in three-qubit Heisenberg model ,entanglement is inexistence in a certain condition x=J/Tlt;-0.7866, coherence is nonexistence only in the condition x=0. Then we study the anisotropy XXZ model base on XX model,the thermal entanglement is nonexistence both in the antiferromagnetic and the ferromagnetic XXZ model when , but the correlation is existent ,and its functional image is changeable with the value of . Finally we discuss concurrence and coherence with changeable magnetic field B in Heisenberg XXZ model, we find that the external uniform magnetic field could induce entanglement in antiferromagnetic system but could not induce entanglement in the ferromagnetic system,and it also could enhance coherence in antiferromagnetic system but it will weaken coherence in the ferromagnetic system.

Keywords: three-qubit ;Heisenberg models; pairwise thermal entanglement ;coherence

目 录

摘要...............................................................I

ABSTRACT.......................................................II

第一章 基本概念及背景...........................................1

1.1 量子纠缠......................................................1

1.2 量子相干......................................................2

1.3 海森堡模型....................................................2

1.4 研究意义......................................................3

1.5 研究现状......................................................4

1.6 本文的研究内容及方法..........................................4

第二章 三量子位海森堡XX模型..................................5

2.1 对热纠缠......................................................5

2.2 量子相干.....................................................12

2.3 对热纠缠和相干性的对比.......................................14

第三章 三量子位海森堡XXZ模型................................16

3.1 对热纠缠.....................................................16

3.2 对热纠缠和相干的对比.........................................19

3.3 磁场的影响...................................................21

第四章 总结......................................................28

附录..............................................................29

参考文献.........................................................39

致谢..............................................................41

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