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Analytic representation of quantum systems
Eissa, Hend A.
Eissa, Hend A.
Publication Date
2016
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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
Faculty of Engineering and Informatics Department of Computing
Awarded
2016
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Abstract
Finite quantum systems with d-dimension Hilbert space, where position x and
momentum p take values in Zd(the integers modulo d) are studied. An analytic
representation of finite quantum systems, using Theta function is considered.
The analytic function has exactly d zeros. The d paths of these zeros on the
torus describe the time evolution of the systems. The calculation of these
paths of zeros, is studied. The concepts of path multiplicity, and path winding
number, are introduced. Special cases where two paths join together, are also
considered. A periodic system which has the displacement operator to real
power t, as time evolution is also studied.
The Bargmann analytic representation for infinite dimension systems, with
variables in R, is also studied. Mittag-Leffler function are used as examples of
Bargmann function with arbitrary order of growth. The zeros of polynomial
approximations of the Mittag-Leffler function are studied.
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Type
Thesis
Qualification name
PhD