Density-functional theory for superfluid systems is developed in the framework of the functional renormalization group based on the effective action formalism. We introduce the effective action for the particle-number and nonlocal pairing densities and demonstrate that the Hohenberg-Kohn theorem for superfluid systems is established in terms of the effective action. The flow equation for the effective action is then derived, where the flow parameter runs from $0$ to $1$, corresponding to the non-interacting and interacting systems. From the flow equation and the variational equation that the equilibrium density satisfies, we obtain the exact expression for the Kohn-Sham potential generalized to including the pairing potentials. The resultant Kohn-Sham potential has a nice feature that it expresses the microscopic formulae of the external, Hartree, pairing, and exchange-correlation terms, separately. It is shown that our Kohn-Sham potential gives the ground-state energy of the Hartree-Fock-Bogoliubov theory by neglecting the correlations. An advantage of our exact formalism lies in the fact that it provides ways to systematically improve the correlation part.
Microscopic description of pair transfer between two superfluid systems (II): a quantum mixing of Time-Dependent Hartree-Fock Bogolyubov trajectories
虽然超流性可以用一个明确打破粒子数对称性的状态来准确地把握，但对重离子反应过程中粒子转移等现象的精确描述只能通过考虑具有良好粒子数的系统来实现。研究了通过混合多个含时Hartree-Fock Bogolyubov（TDHFB）轨迹来恢复多体动力学问题中粒子数的可能性。在我们的方法中，每个轨道是独立的，从变分原理推导出轨道之间的量子混合。相关理论可以被看作是多配置TDHFB（MC-TDHFB）理论的简化版本。它的准确性，以解决问题的对称性恢复动力学问题的情况下，两个超流系统，交换粒子在短时间内。在参考文献[Phys. Rev. C 97，034627（2018）]中，使用一个示意性模型，其中最初由配对哈密顿算子描述的两个系统在短接触时间内耦合，证明了TDHFB轨迹的统计混合只能定性地描述转移过程，并且必须进行完全量子处理。我们在这里表明，目前的MC-TDHFB方法给出了一个很好的协议与精确解时，两种超流体是相同的（对称的情况下）或不同的（不对称的情况下）和从弱到强相互作用强度。最后，我们讨论了这种方法的优点和瓶颈，鉴于其应用于现实系统。
