arXiv 1105.61002011-05hep-thcond-mat.supr-con

约瑟夫森结与AdS/CFT网络

Josephson Junctions and AdS/CFT Networks

Elias Kiritsis, Vasilis Niarchos

备注：: 39 pages, 11 figures; v2 clarified the nature and computation of the Josephson current in subsec. 3.2 and specific properties of the two-site system, analogous minor modifications in subsec. 4.4 and added a new subsec. 4.5 with a new fig. 6
发表信息：: JHEP 1107:112,2011
DOI：: 10.1007/JHEP07(2011)112

摘要：

我们提出了一个新的全息模型的约瑟夫森结（及其网络）的基础上设计的多重引力，即多（超）引力理论的产品不同的渐近AdS时空耦合的混合边界条件。我们提出了一个简单的模型，一个约瑟夫森结（JJ），表现出众所周知的电流相位正弦关系的JJ。在一维全息超导体链中，我们发现库珀对凝聚可以用离散的薛定谔方程来描述。这种不可积方程在过去的凝聚态和光学应用中得到了广泛的研究，已知其表现出复杂的行为，包括周期和准周期解、混沌动力学、孤子和扭结解。在我们的设置中，这些解决方案转化为网络中强耦合超导体的全息配置，具有弱的站点到站点的相互作用，表现出有趣的调制超导模式。在连续极限下，我们的方程简化为Gross-Pitaevskii方程的推广。我们评论的许多可能的扩展和应用这种新的方法。

英文摘要：

We propose a new holographic model of Josephson junctions (and networks thereof) based on designer multi-gravity, namely multi-(super)gravity theories on products of distinct asymptotically AdS spacetimes coupled by mixed boundary conditions. We present a simple model of a Josephson junction (JJ) that exhibits the well-known current-phase sine relation of JJs. In one-dimensional chains of holographic superconductors we find that the Cooper-pair condensates are described by a discretized Schrodinger-type equation. Such non-integrable equations, which have been studied extensively in the past in condensed matter and optics applications, are known to exhibit complex behavior that includes periodic and quasiperiodic solutions, chaotic dynamics, soliton and kink solutions. In our setup these solutions translate to holographic configurations of strongly-coupled superconductors in networks with weak site-to-site interactions that exhibit interesting patterns of modulated superconductivity. In a continuum limit our equations reduce to generalizations of the Gross-Pitaevskii equation. We comment on the many possible extensions and applications of this new approach.

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