A Case Study with an Attractive BEC: Comparison of Lattice Model, Gross–Pitaevskii, and MCTDHB Predictions on a Tunneling Process
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This chapter compares the exact MCTDHB predictions to solutions of the Schrödinger equation with the Bose–Hubbard Hamiltonian computed with the time-evolved block decimation and the mean-field discrete non-linear Schrödinger equation for a tunneling setup. It is found that the discrete model Hamiltonians either make qualitatively unreliable predictions for the many-body physics when mapped to the continuous space setup or that there is no continuous space equivalent of the lattice predictions. In conclusion, exact and self-consistent continuous space many-body methods such as MCTDHB are crucial for the proper description of tunneling to open space problems.
KeywordsContinuous Space Lattice Potential Tunneling Process Escape Time Wannier Function
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