论文标题
使用移位的Krylov方法，用于有限温度的Hartree-fock-Bogoliubov计算的坐标空间求解器
Coordinate-space solver for finite-temperature Hartree-Fock-Bogoliubov calculation using the shifted Krylov method
论文作者
论文摘要
为了研究原始恒星的结构以及在随后的冷却阶段的结构，在各个阶段中计算不均匀的热和冷核物质是非常有趣的。有限温度的Hartree-fock-Bogoliubov（FT-HFB）理论是为此目的的主要选择，但是，在三个维度上，其对超氟（超导）多效系统的数值计算需要巨大的计算成本。为了研究热和冷中子星的外壳中的各种阶段，我们提出了一种有效的方法，可以使用三维（3D）坐标空间表示进行FT-HFB计算。最近，已经提出了一种基于Green功能的轮廓积分的有效方法，该方法已提出[Phys] [Phys。 Rev. C 95，044302（2017）]。我们使用移动的共轭 - 正交共轭方法将方法扩展到有限温度。我们基准在有限温度下中子恒星的内壳中，用于热分离的核和FCC相的FT-HFB计算的3D坐标空间求解器。证明了本方法的计算性能。 $^{146} $ ba确认了四极杆和八极变形的不同关键温度。检查了形状共存功能在$^{184} $ hg中的鲁棒性。对于中子星形壳，嵌入在超氟的低密度中子中子中的变形的富含中子的SE核以0.045 fm $^{ - 3} $和$ k_b t = 200 $ kev的温度出现在FCC相中。在有限温度下，已证明了发达求解器的效率和不均匀的核物质。它可以为核物理学提供标准工具，尤其是对于冷热中子星的结构。
In order to study structure of proto-neutron stars and those in subsequent cooling stages, it is of great interest to calculate inhomogeneous hot and cold nuclear matter in a variety of phases. The finite-temperature Hartree-Fock-Bogoliubov (FT-HFB) theory is a primary choice for this purpose, however, its numerical calculation for superfluid (superconducting) many-fermion systems in three dimensions requires enormous computational costs. To study a variety of phases in the crust of hot and cold neutron stars, we propose an efficient method to perform the FT-HFB calculation with the three-dimensional (3D) coordinate-space representation. Recently, an efficient method based on the contour integral of Green's function with the shifted conjugate-orthogonal conjugate-gradient method has been proposed [Phys. Rev. C 95, 044302 (2017)]. We extend the method to the finite temperature, using the shifted conjugate-orthogonal conjugate-residual method. We benchmark the 3D coordinate-space solver of the FT-HFB calculation for hot isolated nuclei and fcc phase in the inner crust of neutron stars at finite temperature. The computational performance of the present method is demonstrated. Different critical temperatures of the quadrupole and the octupole deformations are confirmed for $^{146}$Ba. The robustness of the shape coexistence feature in $^{184}$Hg is examined. For the neutron-star crust, the deformed neutron-rich Se nuclei embedded in the sea of superfluid low-density neutrons appear in the fcc phase at the nucleon density of 0.045 fm$^{-3}$ and the temperature of $k_B T=200$ keV. The efficiency of the developed solver is demonstrated for nuclei and inhomogeneous nuclear matter at finite temperature. It may provide a standard tool for nuclear physics, especially for the structure of the hot and cold neutron-star matters.
