Numerical investigations of Bose -Einstein condensation in trapped dilute gases and other topics.
Item
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Title
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Numerical investigations of Bose -Einstein condensation in trapped dilute gases and other topics.
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Identifier
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AAI9986353
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identifier
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9986353
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Creator
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Lu, Meng.
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Contributor
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Adviser: Joseph L. Birman
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Date
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2000
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Language
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English
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Publisher
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City University of New York.
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Subject
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Physics, Condensed Matter
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Abstract
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In the first part of the thesis, the phenomenon of Bose-Einstein condensation of trapped dilute gases is investigated mainly using various numerical approaches. Mean field theory provides a framework to understand many features of the condensation. At zero temperature, the equation for the condensate ground state is derived and solved to obtain many properties of the system, such as density profile and various energies. The lowest excitation is obtained using Bogoliubov theory and shows excellent agreement with the experiments. At non-zero temperature, the ground state and the excited states have to be solved self-consistently by using the Popov approximation. The semi-classical approximation is used to simplify the calculation and the condensation fraction is obtained. We further extend the mean field theory to double condensates. The ground state is obtained and the separation of components is simulated based on the derived coupled equations. The research results presented in this part require a wide set of numerical techniques, such as solution of linear algebraic equations, integration of functions, muti-dimensional root finding, solutions to eigenvalue problems, and propagation of partial differential equation with initial values. Some comparisons are given with the experiments.;In the second part of the thesis, I present the research results for two subjects. (a) The scattering probabilities of hot excitons in narrow quantum wells (QWs) are obtained. The exciton-phonon matrix element is considered by using an envelope function Hamiltonian approach in the strong quantization limit where the QW width is smaller than the exciton bulk Bohr radius. The Frohlich-like interaction is taken into account and the contribution of the confined and interface modes to the scattering probability are calculated as a function of quantum well width, electron and hole effective masses, and in-plane center-of-mass kinetic energy. Inter- and intra-subband excitonic transitions are discussed in term of the phonon scalar potential selection rules. Comparison with the experiment is given. (b) The ground state of a few electron quantum dot is obtained using an exact numerical calculation based on the second quantized Hamiltonian.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
