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For a simple 1D model Hamiltonian the NLSE solutions are calculated for positive scattering length. The external potential consists of two potential barriers separated by a well.
Complex scaling is used for calculating the complex chemical potential and the corresponding mean complex energy which are associated with the tunneling of the condensate through the potential barriers.
Assuming that the condensate consists of 2 atoms only, the exact complex scaling variational solutions were obtained. The natural expansion analysis provided us the overlap between the exact variational solution with the best separable wavefuction, as function of the scattering length. The NLSE solutions and the best separable solutions are compared as the scattering length is varied. The motivation behind these computations is to check the validity of the assumption that all atoms in the condensate occupy one orbital only. |