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arXiv 1605.04092hep-th
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反德西特空间中超导系统的涌现

The Emergence of Superconducting Systems in Anti-de Sitter Space

W. M. Wu, M. P. Pierpoint, D. M. Forrester, F. V. Kusmartsev

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10 pages, 2 figures
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摘要：

本文研究了Anti-de Sitter空间$\rm AdS_4$中的（3+1）维引力模型与$\rm AdS_4$渐近平坦边界上（无引力）的（2+1）维超导系统之间的数学关系.我们考虑一个简单的情况下的第二类超导模型（根据金斯堡-朗道理论）与外部垂直磁场${\bf H}$。在拉格朗日系统中引入相互作用势$V(r,ψ) = α(T)|ψ|^2/r^2+χ|ψ|^2/L^2+β|ψ|^4/(2 r^k )$。当超导系统接近转变温度$T_c$时，这在模型内提供了更大的灵活性。总之，我们的结果表明，这两个Ginzburg-Landau微分方程可以直接从爱因斯坦的广义相对论推导出来。

英文摘要：

In this article, we investigate the mathematical relationship between a (3+1) dimensional gravity model inside Anti-de Sitter space $\rm AdS_4$, and a (2+1) dimensional superconducting system on the asymptotically flat boundary of $\rm AdS_4$ (in the absence of gravity). We consider a simple case of the Type II superconducting model (in terms of Ginzburg-Landau theory) with an external perpendicular magnetic field ${\bf H}$. An interaction potential $V(r,ψ) = α(T)|ψ|^2/r^2+χ|ψ|^2/L^2+β|ψ|^4/(2 r^k )$ is introduced within the Lagrangian system. This provides more flexibility within the model, when the superconducting system is close to the transition temperature $T_c$. Overall, our result demonstrates that the two Ginzburg-Landau differential equations can be directly deduced from Einstein's theory of general relativity.

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