Hartee-Fock-Bogoliubov Eigenvalue Problem with Applications in Computational Physics

master's thesis

• Title (croatian): Hartree-Fock-Bogoliubov problem vlastite vrijednosti s primjenama u računalnoj fizici
• Author: Antonio Bjelčić
• Mentor: Zlatko Drmač (mentor)
• Committee member: Zlatko Drmač (predsjednik povjerenstva)
• Committee member: Miljenko Marušić (član povjerenstva)
• Committee member: Zvonimir Bujanović (član povjerenstva)
• Committee member: Maja Resman (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-09-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Constrained Hartree-Fock-Bogoliubov (CHFB) teorija se danas smatra jednom od najuspješnijih metoda za teorijska istraživanja nuklearne strukture. U numeričkim simulacijama, javlja se potreba za efikasnim računanjem spektralne dekompozicije matrice Routhiana. Unatoč tome što matrica Routhiana posjeduje dodatnu podstrukturu, ona nije iskorištena u trenutno dostupnim programskim paketima za numeričke simulacije u okviru CHFB teorije. U ovom radu predložen je algoritam za računanje spektralne dekompozicije matrice Routhiana, koji efikasno iskorištava dodatnu tzv. kvaternionsku podstrukturu. Provedeni numerički testovi demonstriraju da je predložena metoda 2.5 puta efikasnija od trenutno korištenog pristupa. Dodatno, dokazana su i neka zanimljiva svojstva CHFB teorije, te je dana i efikasna implementacija Paige-Van Loan algoritma za dijagonalizaciju kvaternionskih matrica.

Abstract (english)

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.

• Keywords: Constrained Hartree-Fock-Bogoliubov (CHFB) teorija; matrica Routhiana; Paige-Van Loan algoritam
• Keywords (english): Constrained Hartree-Fock-Bogoliubov (CHFB) theory; Routhian matrix; Paige-Van Loan algorithm
• Language: croatian
• URN:NBN: urn:nbn:hr:217:736929
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-02-25 11:48:25