超导体的电动力学：零温下从洛伦兹到伽利略
Electrodynamics of superconductors: from Lorentz to Galilei at zero temperature
AI总结：
本文从洛伦兹不变的Cooper对玻色子模型出发，推导了零温下超导体的电动力学，在非相对论极限下获得伽利略不变的超导系统，并预测了静电场的London穿透长度衰减及有质量电磁场的修正D'Alembert方程。
摘要：
我们讨论了从洛伦兹不变的Cooper对玻色子模型推导超导体与电磁场耦合的电动力学。我们的结果是在零温下获得的，根据热力学第三定律，此时系统的熵为零。在非相对论极限下，我们得到了一个伽利略不变的超导系统，它与人们熟悉的类薛定谔系统有所不同。从这个观点来看，它与费米子的Pauli方程有相似之处，后者是由Dirac方程在非相对论极限下推导出来的，并且与薛定谔方程相比包含一个自旋-磁场项。我们模型的一个独特效应是，超导体内部静电场的衰减恰好具有London穿透长度。此外，我们的理论预测，即使在非相对论超导物质的情况下，有质量的电磁场也满足修正的D'Alembert方程。我们强调了Nambu-Goldstone相位场的作用，它对于获得超导物质场的集体模式至关重要。在非相对论中性超流体的特殊情况下，我们发现了无能隙的类Bogoliubov谱，而对于带电超流体，我们获得的色散关系由等离子体频率打开能隙。
英文摘要：
We discuss the derivation of the electrodynamics of superconductors coupled to the electromagnetic field from a Lorentz-invariant bosonic model of Cooper pairs. Our results are obtained at zero temperature where, according to the third law of thermodynamics, the entropy of the system is zero. In the nonrelativistic limit we obtain a Galilei-invariant superconducting system which differs with respect to the familiar Schrödinger-like one. From this point of view, there are similarities with the Pauli equation of fermions which is derived from the Dirac equation in the nonrelativistic limit and has a spin-magnetic field term in contrast with the Schrödinger equation. One of the peculiar effects of our model is the decay of a static electric field inside a superconductor exactly with the London penetration length. In addition, our theory predicts a modified D'Alembert equation for the massive electromagnetic field also in the case of nonrelativistic superconducting matter. We emphasize the role of the Nambu-Goldstone phase field which is crucial to obtain the collective modes of the superconducting matter field. In the special case of a nonrelativistic neutral superfluid we find a gapless Bogoliubov-like spectrum, while for the charged superfluid we obtain a dispersion relation that is gapped by the plasma frequency.
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