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Many-body methods within the nuclear Lipkin model
Folprecht, Radek ; Knapp, František (advisor) ; Kvasil, Jan (referee)
Title: Many-body methods within the nuclear Lipkin model Author: Radek Folprecht Institute: Institute of Particle and Nuclear Physics Supervisor: Mgr. František Knapp Ph.D., Institute of Particle and Nuclear Physics Abstract: The subject of the present thesis is the Lipkin model, a two- level degenerated quantum system enhanced by two-body interactions. The exact solutions and properties of the model are reviewed and summarized. Several many-body methods common in nuclear physics are used to solve the eigenvalue problem of the time-independent Schrödinger equation. The many-body methods applied to the Lipkin model in the present thesis are the Hartree-Fock mean-field method, the random phase approximation, the Tamm-Dancoff approximation, and the Bardeen-Cooper-Schrieffer method. We propose an instructive iterative extension to the random phase approxi- mation method. For the listed methods, we provide a comprehensive com- parison of the approximation quality for either the ground state energy or excited state energies. Keywords: Lipkin model, Hartree-Fock mean-field method, random phase approximation, Bardeen-Cooper-Schrieffer method 1
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