Dynamics and stability of Bose-Einstein condensates with attractive 1/r interaction
arXiv:0803.1799 · doi:10.1103/PhysRevA.78.013615
Abstract
The time-dependent extended Gross-Pitaevskii equation for Bose-Einstein condensates with attractive 1/r interaction is investigated with both a variational approach and numerically exact calculations. We show that these condensates exhibit signatures known from the nonlinear dynamics of autonomous Hamiltonian systems. The two stationary solutions created in a tangent bifurcation at a critical value of the scattering length are identified as elliptical and hyperbolical fixed points, corresponding to stable and unstable stationary states of the condensate. The stable stationary state is surrounded by elliptical islands, corresponding to condensates periodically oscillating in time, whereas condensate wave functions in the unstable region undergo a collapse within finite time. For negative scattering lengths below the tangent bifurcation no stationary solutions exist, i.e., the condensate is always unstable and collapses.
Corrected the original usage of two inconsistent energy units in some equations and in Figs. 2, 4, 5, and 6; 12 pages 12 figures
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