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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 | |
| dc.identifier.citation | [1]. H. Bethe, Zur Theorie der Metalle I. Eigenwerte und Eigenfunktionen der Linear Atomkette, Zeitschrift für Physik 71, 205-26, (1931).
[2]. Emery, V. J.(1979). New York and London, pp. 247. Plenum press. [3]. A. Klümper, A. Schadschneider and J. Zittarg; Z. Phys. B87,281 (1992). [4]. Affeck, I. (1988). In Fields, Strings and Critical Phenomena (ed. E. Brezin and J. Zinn-Justin), Amsterdam, pp.563. Elsevier Science. [5]. R. K. Bullough, Journal of Modern Optics (2000), vol. 47, No. 11, pp. 2029-2065. Erratum: idbd. (2001), vol. 48, No. 4, pp. 747-748. [6]. W. P. Su; J. R. Schrieffer and A. J. Heeger; Phys. Rev. Lett. 42, 1698 (1979) [7]. Thierry Dauxois & Michel Peyrard, Physics of Solitons, Cambridge University Press 2006. [8]. Kerson Huang, Quantum Field Theory:From Operators to Path integrals,John Wiley & sons, Inc. (1998). [9]. Lewis H. Ryder, Quantum Field Theory, Section edition, Cambridge University Press (1996). [10]. Anthony Osborne, Journal of Mathematical Physics, 19(7), pp.1573, July 1978. [11]. Alan C. Bryan, etc., Letters in Mathematical Physics 3,pp.265(1979). [12]. Alan C. Bryan, etc., Letters in Mathematical Physics 2,pp.445(1978). [13]. A. C. Bryan,etc., IL Nuovo Cimento, Vol. 58B, N.1, pp.1(1980). [14]. Alan. C. Bryan, etc. Complex extensions of a submanifold of solutions of the Sine-Gordon Equation. no press. search in computer. [15]. Ryogo Hirota, Journal of the Physical Society of Japan, Vol. 33, No. 5, 1459, November, 1972. [16]. Graham Bowtell & Allan E. G. Stuart, Physical Review D15, No. 12, 3580(1977). [17]. Sidney Coleman, Physical Review D11, 2088(1975). [18]. S. Mandelstam, Physical Review D11, 3026(1975). [19]. M. G. Forest, etc. SIAM J. Appl. Math. vol.52, No.3, pp. 746-761 (1992). [20]. A.M.Wazwaz, Applied Mathematics and Computation 177,755(2006) [21]. D. J. Thouless, Phy. Rev. B27, 6083 (1983). [22]. Q. Niu and D. J. Thouless, J. Phys. A, 17, 2453 (1984). [23]. P. W. Brouwer, Phys. Rev. B58, 10135 (1998). [24]. T. A. Shutenko, I. L. Aleiner and B. L. Altshuler, Phys. Rev. B61, 10366 (2000). [25]. Y. Levinson, Entin-O.Wohlman and P. Wolfe, Physica A302, 335 (2001); Wohlman-O.Entin and A. Aharony, Phys. Rev. B66, 35329 (2002). [26]. M. Blaauboer, Phys. Rev. B65, 235318 (2002). [27]. J. Wang and B. Wang, Phys. Rev. B65, 153311 (2002); B. Wang and J. Wang, Phys. Rev. B66, 201305 (2002). [28]. P. Sharma and C. Chamon, Phys. Rev. Lett. 87, 96401 (2001) and cond-mat/0209291. [29]. R. Citro, N. Anderi and Q. Niu, cond-mat/0306181. [30]. D. J. Thouless, M. Kohmoto, M. P. Nightingale and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982). [31]. B. I. Halperin, Phys. Rev. B25, 2185 (1982). [32]. Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993) [33]. Y. Hatsugai, Phys. Rev. B48, 1185 (1993). [34]. R. Shindou, J. Phys. Soc.Jpn. 74, 1214 (2005). [35]. C. L. Kane and E. J. Mele , Phys. Rev. Lett. 95, 146802 (2005). [36]. L. Fu and C. L. Kane, Phys. Rev. B74, 195312 (2006). [37]. E. Fradkin, 'Field Theories of Condensed Matter Systems', Addison-Wesley, Redwood City, CA (1991). [38]. N. Nagaosa, 'Quantum Field Theory in Stongly Correlated Electronic Systems', Springer-Verlag, Berlin (1999). [39]. A. O. Gogolin, A. A. Nersesyan and A. M. Tsvelik, 'Bosonization and Strongly Correlated Systems', Cambridge University Press (1998). [40]. T. Giamarchi, 'Quantum Physics in One Dimension', Oxford University Press (2004). [41]. G. Costabile et. al., App. Phys. Lett. 32, 587 (1978). [42]. R. M. DeLeonardis et. al., J. App. Phys. 51, 1211(1980). [43]. R. M. DeLeonardis et. al., J. App. phys. 53, 699 (1982). [44]. Derek. F. Lawden, 'Elliptic Function and Application', Springer-Verlag NY (1989). [45]. R.B.Laughlin, Physical Review B23, 5632 (1981). [46]. Xiao-Liang Qi,etc. arXiv: cond-mat/0604071v2[cond-mat.mes-hall]5 Apr 2006 [47]. Quantum spin pump on a finite antiferromagnetic chain through bulk states. Nan-Hong Kuo, etc, arXiv:0809.2185v1, [cond-mat.str-el] 12 Sep 2008.. [48]. Double sine-gordon chain,C.A.Condat,etc.,Physical Review B,vol.27,number 1,pp.474,1983. [49]. Kink-antikink interactions in the Double sine-gordon equation,D.C.Campbell,etc.,Physica 19D,165(1986) [50]. Zuntao,Fu,etc.Z.Naturforsch.60a,301(2005). [51]. R. K. Bullough and P. J. Caudrey,'Solitons', Springer-Verlag Berlin Heidelberg (1980). [52]. G.Mussardo;V.Riva;G.Sotkov,Nuclear Physics B687,pp.189(2004) [53]. G.Takacs;F.Wagner,Nuclear Physics B741,pp.353(2006) [54]. G.Delfino,etc.,Nuclear Physics B516,pp.675(1998) [55]. G.Delfino,etc.,Nuclear Physics B473,pp.469(1996) | |
| 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.subject | (雙) Sine-Gordon方程式 | zh_TW |
| dc.subject | bius轉換 | zh_TW |
| dc.subject | M&ouml | zh_TW |
| dc.subject | 量子自旋傳輸 | zh_TW |
| dc.subject | Sine-Gordon Equation | en |
| dc.subject | Double Sine-Gordon Equation | en |
| dc.subject | Quantum spin transport | 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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