Time-dependent variational approach for Bose-Einstein condensates with nonlocal interaction

Haas, Fernando and Eliasson, Bengt (2018) Time-dependent variational approach for Bose-Einstein condensates with nonlocal interaction. Journal of Physics B: Atomic, Molecular and Optical Physics, 51. 175302. ISSN 0953-4075 (https://doi.org/10.1088/1361-6455/aad629)

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The nonlinear dynamics of self-bound Bose-Einstein matter waves under the action of an attractive nonlocal and a repulsive local interaction is analyzed by means of a time-dependent variational formalism. The mean-field model described by the Gross-Pitaevskii equation is reduced to a single second-order conservative ordinary differential equation admitting a potential function. The stable fixed points and the linear oscillation frequencies of the breather modes are determined. The chosen nonlocal interactions are a Gaussian-shaped potential and a van der Waals-like potential. The variational solutions are compared with direct numerical simulations of the Gross-Pitaevskii equation, for each of these nonlocalities. The spatio-temporal frequency spectra of linear waves are also determined.