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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References
J.A. Glick, L.D. Carr, Macroscopic Quantum Tunneling of Solitons in Bose–Einstein Condensates. ArXiv e-prints (May 2011). ArXiv:1105.5164
B. Schmidt, M. Fleischhauer, Exact numerical simulations of a one-dimensional trapped Bose gas. Phys. Rev. A 75, 21601 (2007)
R. Hanbury Brown, R.Q. Twiss, A Test of a New Type of Stellar Interferometer on Sirius. Nature 178(1046), 1956 (1048)
R. Hanbury Brown, R.Q. Twiss, Interferometry of the Intensity Fluctuations in Light. I. Basic Theory: The Correlation between Photons in Coherent Beams of Radiation. Proc. Roy. Soc. Lond. A 242(1230), 300324 (1957)
R. Hanbury Brown, R.Q. Twiss, Interferometry of the Intensity Fluctuations in Light. II. An Experimental Test of the Theory for Partially Coherent Light. Proc. Roy. Soc. Lond. A 243(1234), 291319 (1958)
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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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