AdS/CFT对应是全息原理的一个具体实现，其阐明anti-de Sitter空间的引力理论与其边界上的共形场论是对应的。目前，证明AdS/CFT对应的正确性还是比较困难的。然而，可以通过在强耦合的凝聚态物理中的应用来检验这个对应关系。如果这个对应是正确的，由于其将引力理论和量子场理论联系起来，其将是理论物理的一个重大发现和进展。本课题将着重两个方面的工作：1.构建约瑟夫森结（SIS）的全息引力模型，分别用解析求解和数值求解来分析这类非均匀全息超导体的相关性质，并考虑高阶引力背景下对全息超导性质的研究。2.利用导数展开方法来研究超流流体力学的高阶传输系数，考虑在引力中加入Gauss-Bonnet因子后超流流体力学中高阶传输系数和其它现象的变化。本课题的开展将有助于凝聚态物理中强耦合问题的解决，为AdS/CFT对应的正确性提供有力证据，帮助我们进一步理解Navier-Stokes问题。

AdS/CFT corresponse is a promising realization of holographic principle which states that a gravity theory is corresponding to the field theory living on its boundary. It is very difficult to prove directly the correctness of AdS/CFT correspondence at this stage. However one can check the correspondence in strong coupling condensed matter physics. If this statement is true, it is a great discovery and progress in physics because it relates that a gravity to the field theory such as quantum field thoery. In the issue we will focus on two aspects: firstly, constructing a holographic model of a Josephson junction with an insulator link. We will study the properties of Josephson junctions by means of the Strum-Liouville analytical methods and numerical methods. Moreover we will investigate the effects of the higher derivative gravity on the Josephson juction. Secondly, studying the higher order transport coefficients of the superfluid hydrodynamics with derivative expansions methods and considering the change of transport coefficients in the higher order gravity with Gauss-Bonnet term. The action of the issue will shed light on the problem of strong coupling condensed matter physics, take a powerful evidence for the AdS/CFT correspondence and help us to uncover the properties of Navier-Stokes problem further。