Quantum Few-Body Physics with the Configuration Interaction Approach: Method Development and Application to Physical Systems

Sammanfattning: This dissertation, based on six included papers, theoretically investigates properties of quantum few-particle systems. An overview of related experimental research - ultra-cold trapped dilute gases, and electrons in quantum dots - is given, followed by a description of some of the studied many-particle phenomena - Bose-Einstein condensation, quantized vortices, Wigner localization and the Tonks-Girardeau gas. As the research results are presented in the included papers, a main part of the text in this thesis sets focus on methodology. Most of the papers involve use of the configuration interaction method, a numerical method which can give approximative eigenvalues and eigenstates of a few-particle Hamiltonian. The research has also involved further development of this method, by use of the Lee-Suzuki approximation. Formal descriptions of the methods are presented, together with a discussion about the numerical implementation. Explicit examples are given in an appendix. Papers I and II investigate properties of a rotating two-component Bose-Einstein condensate, in particular emerging vortex structures and associated wavefunctions. Paper III demonstrates that the Lee-Suzuki approximation, initially developed in the field of nuclear structure theory, can be useful to describe short-range particle-particle correlations in a trapped bosonic gas. Paper IV investigates the possibility to observe Wigner localization in a nanowire quantum dot, and compares predicted electron transport properties with experimental measurements. Paper V analyzes structures of ultra-cold atoms or molecules with dipolar interactions, in a quasi-one-dimensional trap. Paper VI also considers cold atoms or molecules with dipolar interactions, but in a quasi-two-dimensional setup, with a focus on the resulting Wigner states' dependence on the anisotropy of the interaction.

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