by Khan, Imran

Abstract (Summary)
This dissertation describes some of the efforts involved in developing a systematic understanding of Quantum many-atom systems with real atomic interactions. Specifically, we develop and a apply a non-perturbative Quantum theory of many-atom systems under a strong long-range interaction. A non-perturbative theory is necessary because the perturbation method cannot adequately describe many-atom systems with strong interactions, especially if the interactions are strong enough to form bound states. The long-range behaviour is of special significance because it determines the universal behaviour of an atomic system. In order to calculate the equation of state, at the Van der Waals length scale, a variance minimized variational Monte Carlo (VMVMC) method is developed. Unlike the standard Monte Carlo method, the VMVMC method minimizes the variance of the energy instead of the energy itself. Minimizing the energy is only suitable for the true ground state of a system; many-atom systems represent highly excited states, so, therefore it is not suitable to minimize the energy and instead the variance is minimized. This concept has been developed by Dr. Gao and it has a wider range of applicability than results based on mean field theory or perturbation theory. Results are presented for few and many-atom systems with or without a trap and for both positive and negative scattering lengths.
Bibliographical Information:


School:University of Toledo

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:quantum bose atoms


Date of Publication:01/01/2007

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