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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 胡崇德 | |
| dc.contributor.author | Nan-Hong Kuo | en |
| dc.contributor.author | 郭南宏 | zh_TW |
| dc.date.accessioned | 2021-06-15T02:48:24Z | - |
| dc.date.available | 2009-08-14 | |
| dc.date.copyright | 2009-08-14 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-08-06 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/44274 | - |
| dc.description.abstract | 我研究一維自旋1/2反鐵磁系統的量子自旋傳輸機制. 我先將此自旋鏈轉換成費米子，再做玻色化近似。最後變成(雙) Sine-Gordon方程式，在第二章我證明解的等價性。考慮外場的變化，我加入絕熱相位並考慮在不同的邊界條件下此方程式的解。還原此解到原來的自旋鏈物理系統. 我觀察到在一般的固定邊界條件下有自旋=1通過整個系統。而此結論不同於一般的結論──自旋是由邊界態來傳輸。這寫在第三章。而在其他等價性不同的邊界條件下，自旋是累積在邊界。其機制不同於前，我也提出一個拓樸圖像。這是第四章的內容。最後在第五章，我利用Möbius轉換找到雙Sine-Gordon方程式含絕熱相位的數值精確解。在有限與無限系統，相對應解也有不同。另外我也討論微擾解的方法。 | zh_TW |
| dc.description.abstract | We studied the spin transport mechanism in a S=1/2 antiferromagnetic chain. The spin chain is mapped into a fermion system, where equation of motion is transformed into a (Double) Sine-Gordon Equation ((D)SGE) with the approach of bosonization. We studied first, the non-interacting case. By varying adiabatically a phase angle ϕ which comes from external fields, the spin states change between the Néel state and dimer state and a quantized spin S=1 is transported by the bulk state from one end of the spin chain to the other. We have also considered the interacting case. I found that it is equivalent to the situation of twisted boundary condition. The spin states possess topological meaning. I also transform the solutions of SGE in Wazwaz [20] into another form we are familiar with. Finally, I use Möbius transformation to numerically solve asymmetric DSGE, which was not solved before. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T02:48:24Z (GMT). No. of bitstreams: 1 ntu-98-D91222008-1.pdf: 1840941 bytes, checksum: 9bd13b0e598bd970d4a1bfe260265721 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | Table of contents:
Chapter1: Introduction (4) 1.1: Quantum physics in one dimension and bosonization 1.1.1: Quantum physics in one dimension 1.1.2: Luttinger liquids and Bosonization 1.1.3: Construct soliton operator for the quantized Sine-Gordon Equation 1.2: Introduction of Sine-Gordon Equation 1.2.1 Traveling solution of Sine-Gordon Equation 1.2.2: The separability of Sine-Gordon Equation 1.2.3: Separable solution of Sine-Gordon Equation and its complex extension 1.2.3.2: complex extension 1.2.4: Exact N-Soliton Solitons of Sine-Gordon Equation 1.2.5: Algebraic Geometry ( finite-zone) solutions of Sine-Gordon Equation Chapter 2: Sine-Gordon equation with asymmetric phase (22) 2.1: Introduction 2.1.1: List Wazwaz’s solutions 2.2: Further study of the states of solitons 2.2.1: Mathematics calculation and lemmas 2.2.2: Conclusions and Results of this section Chapter 3: Evident of spin pump through bulk state by solving (28) asymmetric Sine-Gordon Equation 3.0: Introduction 3.1: Hamiltonian and Continuum field theoretical studies 3.2: Analysis of sine-Gordon equation on a finite chain 3.3: Detailed analysis of the static soliton case 3.3.1: The solutions fit the fixed boundary conditions and the energy 3.3.2: Other solutions with the same Ath, x0, energy 3.4: Spin transport 3.5: Spin transport phenomena connecting to source and drain Chapter 4: Sine-Gordon Equation with twisted boundary condition (47) 4.0:Introduction 4.1: Hamiltonian 4.2: Different views of relation between beta and Ath 4.3: Twisted boundary condition of Sine-Gordon Equation 4.4: Real solutions in the forbidden region 4.4.1: Arguments that the state in the forbidden region is real 4.4.2: The energy formula in twised boundary condition SGE 4.5: Another observation in the forbidden region 4.6: Arguments that the spin state in the forbidden region is edge state and the topology view of this case 4.7: Conclusions Chapter 5: Asymmetrical double-sine-Gordon equation (59) 2 5.1: Introduction: 5.2: Classical solutions of Double Sine-Gordon Equation 5.2.1: List of classical solutions of DSGE 5.2.2: List of energies of classical solutions in DSGE 5.2.3: A method to construct solutions and action E of Double Sine-Gordon Equation 5.3: General Mathematical Analysis include easier case: eta<1/4 5.3.1: Potential analysis and related topi 5.3.2: The equation to be solved 5.3.3: Function form and equations for infinite systems 5.3.4: Particular problem occur in eta<1/4 5.3.5.Another method to solve asymmetric Double Sine-Gordon Equation: 5.3.6 Discuss and Conclusion of DSGE in an infinite system 5.4: asymmetric Double Sine-Gordon Equation in finite system (87) 5.4.1: Equations of asymmetric DSGE in a finite system 5.4.2: The particular problem: two sets of parameters for the solutions in finite system 5.5: Perturbation method for approach 0: 5.5.1: Introduction: 5.5.2: Perturbation for a finite system 5.5.3: Three examples of perturbation method 5.6: Discussion and Conclusion of DSGE in an infinite and a finite system Chapter 6: Conclusions (105) Appendix A: Basic properties of Jacobi Elliptic Functions Appendix B: Periodic theorem of static soliton of SGE Appendix C: Introdction to Mo References: | |
| dc.language.iso | en | |
| dc.title | 一維Sine-Gordon方程式和量子自旋傳輸 | zh_TW |
| dc.title | Sine-Gordon Equation and Quantum spin transport in one-dimension | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 郭光宇,高英哲,吳文欽,栗育文,栗育力,朱仲夏 | |
| dc.subject.keyword | (雙) Sine-Gordon方程式,量子自旋傳輸,M&ouml,bius轉換, | zh_TW |
| dc.subject.keyword | Double Sine-Gordon Equation,Sine-Gordon Equation,Quantum spin transport, | en |
| dc.relation.page | 112 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-08-06 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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