| The extended Gross-Pitaevskii equation for the Bose-Einstein condensation of gases with long-range interactions has a second solution which is born together with the ground state in a tangent bifurcation. At the bifurcation point both states coalesce, i.e., the energies and the wave functions are identical. This bifurcation point is in fact an exceptional point and its vicinity in parameter space exhibits a rich variety of phenomena. In particular dipolar condensates can, e.g., show structured ground state wave functions or pitchfork bifurcations of stationary states. In this talk the exceptional points appearing in the nonlinear Gross-Pitaevskii equation are identified and discussed. It is shown that the mean field energy, the chemical potential, and the wave functions exhibit the same behavior as an exceptional point in a linear, nonsymmetric system. A review of the effects appearing in the vicinity of the exceptional points is given. |
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