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arXiv 1509.01769hep-thcond-mat.supr-congr-qc
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暗物质扇区对全息相变影响的解析研究

Analytic investigation of holographic phase transitions influenced by dark matter sector

Lukasz Nakonieczny, Marek Rogatko, Karol. I. Wysokinski

摘要:

解析地研究了s波全息绝缘体/超导体和金属/超导体之间的相变。用变分法求解了U(1)-规范场的暗物质扇区与Maxwell场耦合理论中的Sturm-Liouville本征值问题。此外,在探测极限,我们调查的边缘稳定模式的标量扰动的AdS孤子背景下,连接磁场中的暗物质部门。我们发现,即使有暗物质扇区,超导转变温度$T_c$也与电荷密度$ρ$的1/3次方成正比。这个值似乎是对窄带超导体中荷电局域对玻色子的玻色-爱因斯坦凝聚的指数2/3的强耦合修正。全息液滴溶液受到与暗物质耦合的影响。有趣的是,在探测极限下,临界化学势随着与暗物质耦合的减少而增加,使得凝聚转变更难出现。

英文摘要:

We analytically study the phase transitions between s-wave holographic insulator/superconductor and metal/superconductor. The problem is solved by the variational method for the Sturm-Liouville eigenvalue problem in the theory with dark matter sector of U(1)-gauge field coupled to the Maxwell field. Additionally in the probe limit we investigate the marginally stable modes of scalar perturbations in the AdS solitonic background, connected with magnetic field in the dark matter sector. We have found that even with dark matter sector the superconducting transition temperature $T_c$ is proportional to charge density $ρ$ in power 1/3. This value seem to be strong coupling modification of the exponent 2/3 known from the Bose - Einstein condensation of charged local pair bosons in narrow band superconductors. The holographic droplet solution is affected by the coupling to the dark matter. Interestingly in the probe limit the critical chemical potential increases with the decreasing coupling to dark matter making the condensation transition harder to appear.

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