Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2007-09-14
Phys. Rev. A 77 (2008) 023625
Physics
Condensed Matter
Other Condensed Matter
10 pages, 16 figures (some with low resolution)
Scientific paper
10.1103/PhysRevA.77.023625
Starting from the spectrum of the radially symmetric quantum harmonic oscillator in two dimensions, we create a large set of nonlinear solutions. The relevant three principal branches, with $n_r=0,1$ and 2 radial nodes respectively, are systematically continued as a function of the chemical potential and their linear stability is analyzed in detail, in the absence as well as in the presence of topological charge $m$, i.e., vorticity. It is found that for repulsive interatomic interactions {\it only} the ground state is {\it linearly stable} throughout the parameter range examined. Furthermore, this is true for topological charges $m=0$ or $m=1$; solutions with higher topological charge can be unstable even in that case. All higher excited states are found to be unstable in a wide parametric regime. However, for the focusing/attractive case the ground state with $n_r=0$ and $m=0$ can only be stable for a sufficiently low number of atoms. Once again, excited states are found to be generically unstable. For unstable profiles, the dynamical evolution of the corresponding branches is also followed to monitor the temporal development of the instability.
Carr Lincoln D.
Carretero-González Ricardo
Frantzeskakis Dimitri J.
Herring G.
Kevrekidis Panagiotis G.
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