论文标题
$^{1} s_ {0} $和$^{3} p_ {2} $ superfluids中的$^{1}的共存阶段
Coexistence phase of $^{1}S_{0}$ and $^{3}P_{2}$ superfluids in neutron stars
论文作者
论文摘要
在中子恒星物质中，存在$^{1} s_ {0} $ superfluids在地壳中的密度较低，而$^{3} p_ {2} $ superfluids据信在核心内部深处的较高密度存在。在后者中，取决于温度和磁场，即单轴列相，D $ _ {2} $ - 双轴列相，或者出现D $ _ {4} $ - 双轴列相。在本文中，我们讨论了$^{1} s_ {0} $和$^{3} p_ {2} $ superfluids的混合物，并找到它们的共存。采用循环扩展和两个中子之间相互作用的弱耦合近似，我们获得了Ginzburg-Landau（GL）自由能，其中$^{1} S_ {0} $和$^{0} $和$^{3} p_ {2} $冷凝物都通过包括在内的coupling ornecter coupling couppling oble。我们分析GL自由能，并获得温度和磁场的相图。 We find that the $^{1}S_{0}$ superfluid excludes the $^{3}P_{2}$ superfluid completely in the absence of magnetic field, they can coexist for weak magnetic fields, and the $^{1}S_{0}$ superfluid is expelled by the $^{3}P_{2}$ superfluid at strong magnetic fields,从而证明了$^{3} p_ {2} $超氟的鲁棒性。我们进一步表明，d $ _ {4} $ - bn阶段涵盖了$^{3} p_ {2} $ superfluity的整个区域，这是耦合术语的结果，与纯$^{3} p _ {2} p _ {2} $ superfluid的情况相反，在此之前仅研究了d $ _} $ _} $ - bn nive nive。因此，d $ _ {4} $ - bn阶段在拓扑上是最有趣的阶段，例如，不仅在磁铁中，而且在普通的中子星中接受半量化的非亚伯涡流。
In neutron star matter, there exist $^{1}S_{0}$ superfluids in lower density in the crust while $^{3}P_{2}$ superfluids are believed to exist at higher density deep inside the core. In the latter, depending on the temperature and magnetic field, either the uniaxial nematic phase, the D$_{2}$-biaxial nematic phase, or the D$_{4}$-biaxial nematic phase appears. In this paper, we discuss a mixture of the $^{1}S_{0}$ and $^{3}P_{2}$ superfluids and find their coexistence. Adopting the loop expansion and the weak-coupling approximation for the interaction between two neutrons, we obtain the Ginzburg-Landau (GL) free energy in which both of the $^{1}S_{0}$ and $^{3}P_{2}$ condensates are taken into account by including the coupling terms between them. We analyze the GL free energy and obtain the phase diagram for the temperature and magnetic field. We find that the $^{1}S_{0}$ superfluid excludes the $^{3}P_{2}$ superfluid completely in the absence of magnetic field, they can coexist for weak magnetic fields, and the $^{1}S_{0}$ superfluid is expelled by the $^{3}P_{2}$ superfluid at strong magnetic fields, thereby proving the robustness of $^{3}P_{2}$ superfluid against the magnetic field. We further show that the D$_{4}$-BN phase covers the whole region of the $^{3}P_{2}$ superfluidity as a result of the coupling term, in contrast to the case of a pure $^{3}P_{2}$ superfluid studied before in which the D$_{4}$-BN phase is realized only under strong magnetic fields. Thus, the D$_{4}$-BN phase is topologically the most interesting phase, e.g., admitting half-quantized non-Abelian vortices relevant not only in magnetars but also in ordinary neutron stars.
