Doctoral Degrees (Physics)
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Browsing Doctoral Degrees (Physics) by browse.metadata.advisor "Geyer, Hendrik B."
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- ItemA duality construction for interacting quantum Hall systems(Stellenbosch : University of Stellenbosch, 2011-03) Kriel, Johannes Nicolaas; Scholtz, Frederik G.; Geyer, Hendrik B.; University of Stellenbosch. Faculty of Science. Dept. of Physics.ENGLISH ABSTRACT: The fractional quantum Hall effect represents a true many-body phenomenon in which the collective behaviour of interacting electrons plays a central role. In contrast to its integral counterpart, the appearance of a mobility gap in the fractional quantum Hall regime is due entirely to the Coulomb interaction and is not the result of a perturbed single particle gap. The bulk of our theoretical understanding of the underlying many-body problem is based on Laughlin’s ansatz wave function and the composite fermion picture proposed by Jain. In the latter the fractional quantum Hall effect of interacting electrons is formulated as the integral quantum Hall effect of weakly interacting quasiparticles called composite fermions. The composite fermion picture provides a qualitative description of the interacting system’s low-energy spectrum and leads to a generalisation of Laughlin’s wave functions for the electron ground state. These predictions have been verified through extensive numerical tests. In this work we present an alternative formulation of the composite fermion picture within a more rigorous mathematical framework. Our goal is to establish the relation between the strongly interacting electron problem and its dual description in terms of weakly interacting quasiparticles on the level of the microscopic Hamiltonian itself. This allows us to derive an analytic expression for the interaction induced excitation gap which agrees very well with existing numerical results. We also formulate a mapping between the states of the free particle and interacting descriptions in which the characteristic Jastrow-Slater structure of the composite fermion ansatz appears naturally. Our formalism also serves to clarify several aspects of the standard heuristic construction, particularly with regard to the emergence of the effective magnetic field and the role of higher Landau levels. We also resolve a long standing issue regarding the overlap of unprojected composite fermion trial wave functions with the lowest Landau level of the free particle Hamiltonian.
- ItemFerromagnetic phase transitions in neutron stars(Stellenbosch : Stellenbosch University, 2012-12) Diener, Jacobus Petrus Willem; Scholtz, Frederik G.; Geyer, Hendrik B.; Hillhouse, Gregory C.; Stellenbosch University. Faculty of Science. Dept. of Physics.ENGLISH ABSTRACT: We consider the ferromagnetic phase in pure neutron matter as well as charge neutral, betaequilibrated nuclear matter. We employ Quantum Hadrodynamics, a relativistic field theory description of nuclear matter with meson degrees of freedom, and include couplings between the baryon (proton and neutron) magnetic dipole moment as well as between their charge and the magnetic field in the Lagrangian density describing such a system. We vary the strength of the baryon magnetic dipole moment till a non-zero value of the magnetic field, for which the total energy density of the magnetised system is at a minimum, is found. The system is then assumed to be in the ferromagnetic state. The ferromagnetic equation of state is employed to study matter in the neutron star interior. We find that as the density increases the ferromagnetic field does not increase continuously, but exhibit sudden rapid increases. These sudden increases in the magnetic field correspond to shifts between different configurations of the charged particle’s Landau levels and can have significant observational consequences for neutron stars. We also found that although the ferromagnetic phase softens the neutron star equation of state it does not significantly alter the star’s massradius relationship. The properties of magnetised symmetric nuclear matter were also studied. We confirm that magnetised matter tends to be more proton-rich but become more weakly bound for stronger magnetic fields. We show that the behaviour of the compressibility of nuclear matter is influenced by the Landau quantisation and tends to have an oscillatory character as it increases with the magnetic field. The symmetry energy also exhibits similar behaviour.