在拓扑缺陷和电磁场存在下超流-超导混合物的相对论动力学及其对中子星的应用
Relativistic dynamics of superfluid-superconducting mixtures in the presence of topological defects and an electromagnetic field with application to neutron stars
摘要：
导出了超流-超导混合体与电磁场耦合的相对论动力学方程。为了明确起见，并考虑到我们的结果可能应用于中子星，我们假设混合物是由超流中子、超导质子和正常电子组成的。质子超导的I型和II型进行了分析，并允许可能存在的中子和质子涡旋（或磁畴的情况下，I型质子超导）。导出的方程忽略了除相互摩擦耗散之外的所有耗散效应，并且对任意温度都有效（即它们并不意味着所有核子都是成对的），这对磁星条件特别重要。结果表明，对于典型的中子星，这些一般方程可以得到很大的简化，并证明了一种磁流体动力学近似的合理性。我们的结果与文献中的非相对论公式进行了比较，发现了一些差异，特别是，它表明，一般情况下，电位移${\pmb D}$不符合电场${\pmb E}$，相反，在以前的作品中所述。这里开发的相对论框架是很容易扩展到更复杂的微观物理模型，它提供了必要的基础，逼真的中子星的建模。
英文摘要：
The relativistic dynamic equations are derived for a superfluid-superconducting mixture coupled to the electromagnetic field. For definiteness, and bearing in mind possible applications of our results to neutron stars, it is assumed that the mixture is composed of superfluid neutrons, superconducting protons, and normal electrons. Proton superconductivity of both I and II types is analysed, and possible presence of neutron and proton vortices (or magnetic domains in the case of type-I proton superconductivity) is allowed for. The derived equations neglect all dissipative effects except for the mutual friction dissipation and are valid for arbitrary temperatures (i.e. they do not imply that all nucleons are paired), which is especially important for magnetar conditions. It is demonstrated that these general equations can be substantially simplified for typical neutron stars, for which a kind of magnetohydrodynamic approximation is justified. Our results are compared to the nonrelativistic formulations existing in the literature and a number of discrepancies are found. In particular, it is shown that, generally, the electric displacement ${\pmb D}$ does not coincide with the electric field ${\pmb E}$, contrary to what is stated in the previous works. The relativistic framework developed here is easily extendable to account for more sophisticated microphysics models and it provides the necessary basis for realistic modelling of neutron stars.
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