Condition for collapse as a function of the initial width v(0) and P values for G = 0 (the bigger strip shaded area) and G = −0.03 (grey shaded area)
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Figure 5. Condition for collapse as a function of the initial width v(0) and P values for G = 0 (the bigger strip shaded area) and G = −0.03 (grey shaded area). The dotted and dashed lines correspond to the equilibrium point for each P in the cases of G = 0 and G = −0.03 respectively.
We take into account the higher-order corrections in two-body scattering interactions within a mean-field description, and investigate the stability conditions and collective excitations of a harmonically trapped Bose–Einstein condensate (BEC). Our results show that the presence of higher-order corrections causes drastic changes to the stability condition of a BEC. In particular, we predict that with the help of the higher-order interaction, a BEC can now collapse even for positive scattering lengths; whereas, a usually unstable BEC with a negative scattering length can be stabilized by positive higher-order effects. The low-lying collective excitations are significantly modified as well, compared to those without the higher-order corrections. The conditions for a possible experimental scenario are also proposed.