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Analytic Representations of Finite Quantum Systems on a Torus

By Muna Jabuni

Abstract

Quantum systems with a finite Hilbert space, where position x and momen-\ud tum p take values in Z(d) (integers modulo d), are studied. An analytic\ud representation of finite quantum systems is considered. Quantum states are\ud represented by analytic functions on a torus. This function has exactly d\ud zeros, which define uniquely the quantum state. The analytic function of a\ud state can be constructed using its zeros. As the system evolves in time, the\ud d zeros follow d paths on the torus. Examples of the paths ³n(t) of the zeros,\ud for various Hamiltonians, are given. In addition, for given paths ³n(t) of the\ud d zeros, the Hamiltonian is calculated. Furthermore, periodic finite quantum\ud systems are considered. Special cases where M of the zeros follow the same\ud path are also studied, and general ideas are demonstrated with several ex-\ud amples. Examples of the path with multiplicity M = 1; 2; 3; 4; 5 are given. It\ud is evidenced within the study that a small perturbation of the initial values\ud of the zeros splits a path with multiplicity M into M different paths.Libyan Cultural Affair

Topics: Finite quantum systems, Torus, Analytic functions, Representation
Publisher: Department of Computing
Year: 2010
OAI identifier: oai:bradscholars.brad.ac.uk:10454/4856
Provided by: Bradford Scholars

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