Quantum Monte Carlo Study Of The Low-dimensional Bose-Einstein Condensation

Bose-Einstein condensation (BEC) is a ubiquitous phenomenon related to many fields in physics. It is very important not only for basic theoretical research but also for the promising applications in techniques. Since BEC was realized in a series of experiments on vapors of 87Rb,23Na,7Li, many physicists had devoted themselves to searching a universal rule to describe the properties of condensate and the dominant factors which influence the properties of condensate in physics. Previous studies mostly focused on the characters of BEC in three-dimensional (3D) systems. However, in the system of reduced dimensionality, thermal and quantum fluctuations are stimulated significantly, resulting in many unique properties absent in 3D system. Some peculiar properties of low-dimensional systems have already been applied to new materials and new devices. For these reasons, the properties of low-dimensional BEC have become a hot subject recently.In the weakly interacting region, the mean-field theory has been successfully used to investigate the effect of interboson interactions on the condensate. However, in the strong interacting region, the mean-field theory does not hold true. The Quantum Monte Carlo (QMC) method does not contain any physical approximation when the interboson interaction is considered. It is suitable for studying the properties of the system with arbitrary interboson interaction strength. In this paper, we study the ground state properties of interacting bosons confined in a two-dimensional harmonic trap and charged bosons confined in a one-dimensional harmonic trap by means of QMC method.The thesis consists of five chapters. Chapter one is the introduction of this paper. In chapter two, we briefly introduce the history of BEC, including the basic theories and relevant experiments. In chapter three, we present the theories and applications of the Quantum Monte Carlo method, and concentrate on the Variational Monte Carlo (VMC) method and the diffusion Monte Carlo (DMC) method. In chapter four, we calculated the ground-state properties of bosons confined in a two-dimensional (2D) harmonic trap by means of VMC method. The results show that there is anomalous depletion of condensate in the centre of trap in the strong interacting region. In character five, we obtain the ground-state properties of charged bosons confined in one-dimensional (1D) harmonic trap, and investigate the"fermionization"of boson gas with strong interaction. This model is instructive for...