Bose-Einstein condensates have been, by now, observed in as many as nine different atomic assemblies of bosons. Such
a condensate is quantum mechanical interacting system whose ground state properties can be studied theoretically by
solving the appropriate non-linear Gross-Pitaevskii-Ginzburg GPG equation. One can now study the change in the
behavior of Bose-Einstein condensate by introducing a localized impurity which interacts with the condensate as a
function of position of impurity in the condensate. The introduction of such an impurity can be mimicked by simply
allowing an intensely focused laser beam to interact with the condensate. This would lead to alteration of ground state
properties of the condensate as it would now interact with a potential of type <i>V Sech</i><sup>2</sup>(r/w) where, <i>V</i> and <i>w</i> are
amplitude and width of the impurity potential, respectively.
The modified GPG equation in the presence of localized impurity potential as function of position in the
condensate, has been numerically solved to obtain its various ground state properties as function of position, such as
total energy per particle, chemical potential, kinetic, harmonic trap potential and two-body interaction energies per
particle in addition to energy associated with impurity potential, correlation length, healing length etc. We have studied
the behavior of the above-mentioned ground state properties as the position of localized impurity is changed in the
condensate from core to peripheral position. While the total, harmonic oscillator potential and impurity energies decrease
as the position of localized impurity is displaced from core of the condensate to its periphery, the value of two-body
inter-particle interaction energy increases. Further, the values of chemical potential and total energy per particle shows
decrease by ~ 9% and ~ 17% respectively, leading to the inference that the stability of condensate increases as the
localized impurity is moved away from the core of the condensate.
Using the density-functional theory, the Ginzburg Pitaevskii Gross (GPG) equation for Bose-Einstein (BE) condensate, confined in a magnetic trap, is modified to include contribution from three-body collisions in the strongly interacting regime a>><i>l</i>, 'a' is the scattering length and '<i>l</i>' being the characteristic low energy length scale. This generalized GPG equation has been solved numerically using the analytically derived Thomas-Fermi order parameter, which also includes three-body interactions. The order parameter, chemical potential, extent of correlation and other ground state properties are computed when the aspect ratio, λ, is varied from1.0 to 0.05 (λ represents the anisotropy of the magnetic trap). As λ is varied from 1.0 to 0.05, the condensate shape changes from isotropic three-dimensional (3-D) to highly anisotropic quasi one-dimensional (1-D). The stability of the BE condensate increases with decrease in λ, which is also borne out by the behavior of chemical potential and the total energy per particle, as there is a decrease of about four times for a=5000 a<sub>0</sub> as well as for a=7000 a<sub>0</sub>, 'a<sub>0</sub>' being the Bohr radius. The extent of correlations, however, increases by more than five folds, showing that quasi 1-D BE condensate is highly correlated. Both two- and three-body interaction energies show a decrease with decrease in λ: three-body interaction energy staying below two-body interaction energy for a=5000 a<sub>0</sub> while for a=7000 a<sub>0</sub>, a cross-over occurs between the two at λ ~ 0.35. As one goes from 3-D to quasi 1-D, the percentage difference for various physical quantities, computed between only two-body interactions and when both two- and three-body interactions are considered, shows a decrease, suggesting that the effect of three-body collisions become increasingly less significant in agreement with the recent study.