Holographic Josephson Junction in Various Dimensions

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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

推文