Ground State of Interacting Many Boson Systems: An Approach Based On Natural Orbitals

摘要

We have developed an alternative approach to investigate the ground state properties of many boson systems with interactions in a harmonic trap. The method is inspired, and to some extent similar to the Kohn-Sham formulation of the density functional theory. The method is applied to a model many boson system to obtain the ground state properties of the system. We give a description of a many boson system within the second quantization formalism. We employ the natural orbitals to describe the ground state of the system. We represent the natural orbitals as an expansion in terms of a complete set. We obtain the expansion coefficients by minimizing the total energy. We apply the proposed method to a model system of interacting bosons. The results are compared with the results obtained from Gross-Pitaevskii equations which are widely used to describe Bose-Einstein Condensation. Also we compare our results with the Monte Carlo simulation results found in the literature. The agreement of our results with the results of Gross-Pitaevskii equations establishes the feasibility and accuracy of the method.