Ultra-soğuk atomik gazların taban-durumu özellikleri

After the observation of Bose-Einstein condensation, the developments in the experimental control and measurement methods provided the realization of basic models of many-body physics using dilute, ultra-cold gases. This thesis presents a theoretical study on a number of topics on ultra-cold atomic gas systems. First, a simple model of trapped, degenerate ultra-cold plasma is presented. Using the variational approach, the dependence of the cloud size on electron density is studied, electron and ion densities are also calculated by means of modified Thomas-Fermi model. Next, the behavior of a single particle hopping on a three dimensional cubic optical lattice in the presence of a Mott insulator of bosons is investigated. Localization problem of a single fermion is studied and effects of lattice anisotropy, and higher impurity bands are also calculated. Then, a two-dimensional condensate with long-range, attractive gravity-like interaction is studied. Ground-state properties, dynamics, and vortex states are analyzed by using a variational approach for thissystem. Finally, the thermodynamics of the harmonically trapped ideal gas obeying generalized exclusion statistics is investigated.