论文标题
Hartree-fock-Bogoliubov参考状态的零配对极限
Zero-pairing limit of Hartree-Fock-Bogoliubov reference states
论文作者
论文摘要
变异的Hartree-fock-Bogoliubov（HFB）平均场理论是用于超级流体系统的各种（从头算）多体方法的起点。当系统闭合 - （子）外壳字符时，将HFB方程的零配对限制构成教科书问题，但通常，每当单颗粒级别的天真填充对应于开放式壳系统时，它通常被认为是错误的定义。 目前的工作表明，HFB状态的零配对极限在数学上是明确定义的，与系统的闭合或开放式特征无关。尽管如此，极限状态的性质在很大程度上取决于基础的壳结构和相关的幼稚填充，而在零对限制的粒子数a中达到的幼稚填充。所有分析结果均已确认并用数值说明。 尽管在过去的几十年中，HFB理论已被正式和数字进行了深入的审查，但它仍然揭示了未知和有些意外的特征。从这个一般角度来看，目前的分析表明，即使在HFB Hamiltonian矩阵中，HFB理论也不会降低到Hartree-Fock理论。
The variational Hartree-Fock-Bogoliubov (HFB) mean-field theory is the starting point of various (ab initio) many-body methods dedicated to superfluid systems. While taking the zero-pairing limit of HFB equations constitutes a text-book problem when the system is of closed-(sub)shell character, it is typically, although wrongly, thought to be ill-defined whenever the naive filling of single-particle levels corresponds to an open-shell system. The present work demonstrates that the zero-pairing limit of an HFB state is mathematically well-defined, independently of the closed- or open-shell character of the system in the limit. Still, the nature of the limit state strongly depends on the underlying shell structure and on the associated naive filling reached in the zero-pairing limit for the particle number A of interest. All the analytical findings are confirmed and illustrated numerically. While HFB theory has been intensively scrutinized formally and numerically over the last decades, it still uncovers unknown and somewhat unexpected features. From this general perspective, the present analysis demonstrates that HFB theory does not reduce to Hartree-Fock theory even when the pairing field is driven to zero in the HFB Hamiltonian matrix.
