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.
