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    Analytic Representations of Finite Quantum Systems on a Torus

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    Publication date
    2011-03-30
    Author
    Jabuni, Muna
    Supervisor
    Vourdas, Apostolos
    Keyword
    Finite quantum systems
    Torus
    Analytic functions
    Representation
    Rights
    Creative Commons License
    The University of Bradford theses are licenced under a Creative Commons Licence.
    Institution
    University of Bradford
    Department
    Department of Computing
    Awarded
    2010
    
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    Abstract
    Quantum systems with a finite Hilbert space, where position x and momen- tum p take values in Z(d) (integers modulo d), are studied. An analytic representation of finite quantum systems is considered. Quantum states are represented by analytic functions on a torus. This function has exactly d zeros, which define uniquely the quantum state. The analytic function of a state can be constructed using its zeros. As the system evolves in time, the d zeros follow d paths on the torus. Examples of the paths ³n(t) of the zeros, for various Hamiltonians, are given. In addition, for given paths ³n(t) of the d zeros, the Hamiltonian is calculated. Furthermore, periodic finite quantum systems are considered. Special cases where M of the zeros follow the same path are also studied, and general ideas are demonstrated with several ex- amples. Examples of the path with multiplicity M = 1; 2; 3; 4; 5 are given. It is evidenced within the study that a small perturbation of the initial values of the zeros splits a path with multiplicity M into M different paths.
    URI
    http://hdl.handle.net/10454/4856
    Type
    Thesis
    Qualification name
    PhD
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