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Analytic Representations of Finite Quantum Systems on a Torus
Jabuni, Muna
Jabuni, Muna
Publication Date
2011-03-30
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The University of Bradford theses are licenced under a Creative Commons Licence.
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Accepted for publication
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.
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Type
Thesis
Qualification name
PhD