Spectral singularities in PT-symmetric Bose-Einstein condensates

We consider the model of a PT-symmetric Bose-Einstein condensate in a delta-function double-well potential. We demonstrate that analytic continuation of the primarily non-analytic term vertical bar psi vertical bar(2)psi-occurring in the underlying Gross-Pitaevskii equation-yields new branch points where three levels coalesce. We show numerically that the new branch points exhibit the behaviour of exceptional points of second and third order. A matrix model which confirms the numerical findings in analytic terms is given.