Hartee-Fock-Bogoliubov Eigenvalue Problem with Applications in Computational Physics
Antonio Bjelčić · 2020
Constrained Hartree-Fock-Bogoliubov (CHFB) theory is considered to be one of the most successful methods for theoretical studies of nuclear structure. In numerical simulations, one often has to find the spectral decomposition of Routhian matrix. Even though the Routhian matrix exhibits a certain substructure, currently used software packages for numerical simulations in the CHFB framework do not utilize it. In this thesis, a new method for diagonalization of the Routhian matrix, which exploits the additional quaternionic substructure, is proposed and tested. Numerical experiments show that the proposed method outperforms, by a factor of 2.5, currently used naive and straightforward approach. Additionally, in this thesis some interesting properties of the CHFB theory are provided, together with an effcient implementation of the Paige-Van Loan algorithm for diagonalization of quaternionic matrices.