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We investigate the dynamical behavior of the Gross-Pitaevskii equation for a Bose-Einstein condensate trapped in a spherical power law potential restricted to the repulsive case, from the dynamical system formalism point of view. A five-dimensional dynamical system is found (due the symmetry of the Gross-Pitaevskii equation interacting with a potential), where the Thomas-Fermi approximation constrains the parameter space of solutions. We show that for values of the power law exponent equal or smaller than 2 the system seems to be stable. However, when the corresponding exponent is bigger than 2, the instability of the system grows when the power law exponent grows, indicating that large values of the aforementioned parameter can be related to a loss in the number of particles from the condensed state. This fact can be used also to show that the stability conditions of the condensate are highly sensitive to the exponent associated with the external potential.
The ground state of a Bose-Einstein condensate in a two-dimensional trap potential is analyzed numerically at the infinite-particle limit. It is shown that the anisotropy of the many-particle position variance along the $x$ and $y$ axes can be opposi
Improved control of the motional and internal quantum states of ultracold neutral atoms and ions has opened intriguing possibilities for quantum simulation and quantum computation. Many-body effects have been explored with hundreds of thousands of qu
We have studied a Bose-Einstein condensate of $^{87}Rb$ atoms under an oscillatory excitation. For a fixed frequency of excitation, we have explored how the values of amplitude and time of excitation must be combined in order to produce quantum turbu
We consider the quasi-particle excitations of a trapped dipolar Bose-Einstein condensate. By mapping these excitations onto radial and angular momentum we show that the roton modes are clearly revealed as discrete fingers in parameter space, whereas
We derive a governing equation for a Kelvin wave supported on a vortex line in a Bose-Einstein condensate, in a rotating cylindrically symmetric parabolic trap. From this solution the Kelvin wave dispersion relation is determined. In the limit of an