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Transitional region of phase transitions in nuclear models

Thesis/Dissertation:

Abstract

The phase transition in an exactly solvable nuclear model, the Lipkin model, is scrutinised, first using Hartree-Fock methods or the plain mean flield approximation, and then using projected wave functions. It turns out that the plain mean field is not reliable in the transitional region. Although the projection methods give better resutls in the transitional region, it leads to spurious singularities. While the energy of the projection before variation is slightly better than its projection after variation counterpart, the perfomance of the wave function is considerably worse in the transitional region. The model's wave function undergoes dramatic changes in the transitional region. The mechanism that brings about these changes is studied within a model Hamiltonian that can reproduce the Lipkin model mathematically. It turns out that the numerous exceptional points found in the transitional region, bring about the change of the ground state wave function. Exceptional points are associated with level crossings in the complex plane. These level crossings can be seen as level repulsions in the spectrum. Level repulsion and a sensitive dependence of the system on some external parameter are characteristics of chaotic behaviour. These two features are found in the transitional region of the Lipkin model. In  More>>
Authors:
Publication Date:
Jan 01, 1988
Product Type:
Thesis/Dissertation
Reference Number:
AIX-20-007259; EDB-89-017759
Resource Relation:
Other Information: Thesis (M.Sc.)
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; NUCLEAR MODELS; PHASE TRANSFORMATIONS; COUPLING; FLUCTUATIONS; HAMILTONIANS; HARTREE-FOCK METHOD; MANY-BODY PROBLEM; QUANTUM MECHANICS; SPIN; SYMMETRY; THEORETICAL DATA; VARIATIONAL METHODS; WAVE FUNCTIONS; ANGULAR MOMENTUM; DATA; FUNCTIONS; INFORMATION; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MECHANICS; NUMERICAL DATA; PARTICLE PROPERTIES; QUANTUM OPERATORS; VARIATIONS; 653001* - Nuclear Theory- Nuclear Structure, Moments, Spin, & Models
OSTI ID:
6572909
Research Organizations:
University of the Witwatersrand, Johannesburg (South Africa)
Country of Origin:
South Africa
Language:
English
Availability:
the Registrar, University of the Witwatersrand, 1 Jan Smuts Avenue, Johannesburg. 2001, South Africa.
Submitting Site:
INIS
Size:
Pages: 144
Announcement Date:

Thesis/Dissertation:

Citation Formats

Kotze, A A. Transitional region of phase transitions in nuclear models. South Africa: N. p., 1988. Web.
Kotze, A A. Transitional region of phase transitions in nuclear models. South Africa.
Kotze, A A. 1988. "Transitional region of phase transitions in nuclear models." South Africa.
@misc{etde_6572909,
title = {Transitional region of phase transitions in nuclear models}
author = {Kotze, A A}
abstractNote = {The phase transition in an exactly solvable nuclear model, the Lipkin model, is scrutinised, first using Hartree-Fock methods or the plain mean flield approximation, and then using projected wave functions. It turns out that the plain mean field is not reliable in the transitional region. Although the projection methods give better resutls in the transitional region, it leads to spurious singularities. While the energy of the projection before variation is slightly better than its projection after variation counterpart, the perfomance of the wave function is considerably worse in the transitional region. The model's wave function undergoes dramatic changes in the transitional region. The mechanism that brings about these changes is studied within a model Hamiltonian that can reproduce the Lipkin model mathematically. It turns out that the numerous exceptional points found in the transitional region, bring about the change of the ground state wave function. Exceptional points are associated with level crossings in the complex plane. These level crossings can be seen as level repulsions in the spectrum. Level repulsion and a sensitive dependence of the system on some external parameter are characteristics of chaotic behaviour. These two features are found in the transitional region of the Lipkin model. In order to study chaos, one has to resort to a statistical analysis. A measure of the chaotic behaviour of systems, the ..delta../sub 3/ statistic, is introduced. The results show that the Lipkin model is harmonic, even in the transitional region. For the Lipkin model the exceptional points are regularly distributed in the complex plane. In a total chaotic system the points would be randomly distributed.}
place = {South Africa}
year = {1988}
month = {Jan}
}