跳到主要內容

簡易檢索 / 詳目顯示

回結果列表
研究生： 陳彥佑
Metta Tan Yan You
論文名稱： Holographic Josephson Junction in Various Dimensions
指導教授： 陳江梅
Chiang-Mei Chen
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2015
畢業學年度： 104
語文別： 英文
論文頁數： 38
中文關鍵詞： 對偶
相關次數： 點閱：14  下載：0 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 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。

    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.

    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

    [1] G. 't Hooft, \Dimensional reduction in quantum gravity," Salamfest 1993:0284-
    296 [gr-qc/9310026].
    [2] L. Susskind, \The World as a hologram," J. Math. Phys. 36, 6377 (1995) [hepth/
    9409089].
    [3] Jacob D. Bekenstein, "Universal upper bound on the entropy-to-energy ratio for
    bounded systems," Phys. Rev. D 23, 287 (1981)
    [4] Stephen Hawking, "Black holes and thermodynamics," Phys. Rev. D 13, 191
    (1976)
    [5] Juan Maldacena, "The large N limit of superconformal eld theories and supergravity,"
    Adv. Theor. Math Phys. 2, 231 (1998) [arXiv: hep-th/9711200]
    [6] Edward Witten, "Anti-de Sitter space and holography," Adv. Theor. Math Phys.
    2, 253 (1998) [arXiv: hep-th/9802150]
    [7] Gubser S. S.,Klebanov I. R. and Polyakov A. M., "Gauge theory correlators from
    non-critical string theory," Phys. Lett. B, 1998, 428: 105 114
    [8] 3eX, "Ä›
    vÊv(ÝZKi-„É(, (2014)" ¶ÑåmúH>
    [9] R. D. Parks, "Superconductivity," Marcel Dekker Inc.(1969)
    [10] E.W. Carlson, V. J. Emery, S. A. Kivelson and D. Orgad, "Concepts in high
    temperature superconductivity," [arXiv: cond-mat/0206217]

    QR CODE
    :::