Entanglement and energy level crossing of spin and Fermi Hamilton operators
- Authors: De Greef, Jacqueline
- Date: 2013-07-24
- Subjects: Quantum entanglement , Spin operators , Hamilton operator , Fermi Hamilton operators , Energy levels (Quantum mechanics) , Quantum theory , Linear operators
- Type: Thesis
- Identifier: uj:7682 , http://hdl.handle.net/10210/8549
- Description: 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.
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Spin Hamilton operators, symmetry breaking, energy level crossing and entanglement
- Authors: Steeb, Willi-Hans , Hardy, Yorick , De Greef, Jacqueline
- Date: 2012-01-27
- Subjects: Hilbert spaces , Hamilton operators , Spin matrices , Eigenvalues
- Type: Article
- Identifier: uj:5975 , http://hdl.handle.net/10210/8440
- Description: © Willi-Hans Steeb, Yorick Hardy and Jacqueline de Greef, 2012 Available online: http://arxiv.org/abs/1110.4204v2 , We study finite-dimensional product Hilbert spaces, coupled spin systems, entanglement and energy level crossing. The Hamilton operators are based on the Pauli group. We show that swapping the interacting term can lead from unentangled eigenstates to entangled eigenstates and from an energy spectrum with energy level crossing to avoided energy level crossing.
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