Abstract
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.
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Lode, A.U.J. (2015). A Case Study with an Attractive BEC: Comparison of Lattice Model, Gross–Pitaevskii, and MCTDHB Predictions on a Tunneling Process. In: Tunneling Dynamics in Open Ultracold Bosonic Systems. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-07085-8_4
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DOI: https://doi.org/10.1007/978-3-319-07085-8_4
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