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Here we collect various methods for going beyond GPE.
DAMOP 2017
Lincoln Carr gave a very nice talk about how bright solitons can demonstrate features that go from GPE to purely quantum. Some of his techniques are available as open-source code projects, especially is OpenMPS project for Matrix Product States. This method is used to show quantum phenomena here Higher-order quantum bright solitons in Bose-Einstein condensates show truly quantum emergent behavior.
He suggests looking at enzyme calculations to see a successful application of matching at various scales. Warns that one method does not properly discuss convergence (fixed lattice with 256 points
Has an HFB code for BEC's he is willing to share.
N. Proukakis is working with ZNG codes. Talk to him and maybe visit.
Simeon Mistakidis gave a poster about Bent Dark Solitons demonstrating some beyond-GPE effects using an expensive variation technique with memory.
Rudi Grimm is looking at Bose-Fermi mixtures.
Single component fermions with BEC
TD-RASSCF: Has GPE and MCTDHFB as limits. (Might be the method Carr was cautious about).