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標題: | 一維Sine-Gordon方程式和量子自旋傳輸 Sine-Gordon Equation and Quantum spin transport in one-dimension |
作者: | Nan-Hong Kuo 郭南宏 |
指導教授: | 胡崇德 |
關鍵字: | (雙) Sine-Gordon方程式,量子自旋傳輸,M&ouml,bius轉換, Double Sine-Gordon Equation,Sine-Gordon Equation,Quantum spin transport, |
出版年 : | 2009 |
學位: | 博士 |
摘要: | 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。 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. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/44274 |
全文授權: | 有償授權 |
顯示於系所單位: | 物理學系 |
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