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. / Libyan Cultural Affairs
| Identifer | oai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/4856 |
| Date | January 2010 |
| Creators | Jabuni, Muna |
| Contributors | Vourdas, Apostolos |
| Publisher | University of Bradford, Department of Computing |
| Source Sets | Bradford Scholars |
| Language | English |
| Detected Language | English |
| Type | Thesis, doctoral, PhD |
| Rights | <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/3.0/"><img alt="Creative Commons License" style="border-width:0" src="http://i.creativecommons.org/l/by-nc-nd/3.0/88x31.png" /></a><br />The University of Bradford theses are licenced under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/3.0/">Creative Commons Licence</a>. |
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