Abstract
M.Sc. (Applied Mathematics)
Entanglement is a quantum resource with applications in quantum communication
as well as quantum computing amongst others. Since quantum entanglement
is such an abstract concept numerous mathematical measures exist. Some
of these have a purely theoretic purpose whereas others play a role in describing
the magnitude of entanglement of a system. In quantum systems energy
level crossing may occur. Energy levels in quantum systems tend to repel each
other so when any type of degeneracy occurs where the energy levels coalesce
or cross it is of interest to us. Two such points of degeneracy are exceptional
and diabolic points. When these occur it is useful to investigate these points in
specific systems and observe level crossing. In this thesis we mainly investigate
the relationship between entanglement, energy level crossing and symmetry as
well as the exceptional and diabolic points of specific systems. We are especially
interested in systems described by spin and Fermi operators.