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姓名 陳彥佑(Metta Tan Yan You)  查詢紙本館藏   畢業系所 物理學系
論文名稱
(Holographic Josephson Junction in Various Dimensions)
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摘要(中) 因 Ginzburg-Landau模型複雜的緣故, 超導特性的模擬一直是一項艱鉅的工作。在2008年 Horowitz 等人應用了AdS/CFT 對偶來模擬了包括超導相變等特性,帶來了AdS/CFT 對偶在實際應用方面的突破,並且提供了一個可以有效研究超導特性的工具。此論文將會利用AdS/CFT對偶來建構出任意維度的約瑟夫森結(Josephson Junction)模型並使用擬值譜法(pseudo-spectral method)來計算出此模型在2與3維的數值解。
摘要(英) Simulation of superconductor properties was deemed as a challenging task in the past due to the complexity of the Ginzburg-Landau Model. In 2009 Horowitz et al applied AdS/CFT Correspondence to simulate the properties of superconductor, which is a breakthrough in terms of the practical application of this theory and potentially provides a convenient tool to look into the properties of superconductor. In this thesis I will apply AdS/CFT to model Josephson junction in any dimensions and use the pseudospectral method to find the numerical solutions to the holographic Josephson junction in 2 and 3 spatial dimensions.
關鍵字(中) ★ 對偶 關鍵字(英) ★ Holographic
★ AdS/CFT
論文目次 1 Introduction 1
1.1 AdS/CFT Correspondence . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Holographic Superconductors . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Josephson Junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Holographic Josephson Junction 5
2.1 Gravitational Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Homogeneous Superconductor . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Holographic Josephson Junction . . . . . . . . . . . . . . . . . . . . . 9
2.4 Coordinate Transformation and Boundary Conditions . . . . . . . . . 12
3 Numerical Results 15
3.1 SNS Josephson Junction . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 SsS Josephson Junction . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Impact of Gap Depth on Maximum Current and Condensate . . . . . 25
4 Conclusion 29
A Analytical Analysis of Critical Chemical Potential 31
i
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指導教授 陳江梅(Chiang-Mei Chen) 審核日期 2015-10-27
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