General relations for quantum gases in two and three dimensions. II. Bosons and mixtures

@article{Werner2012GeneralRF,
  title={General relations for quantum gases in two and three dimensions. II. Bosons and mixtures},
  author={F'elix Werner and Yvan Castin},
  journal={Physical Review A},
  year={2012},
  volume={86},
  pages={053633}
}
We derive exact general relations between various observables for N bosons with zero-range interactions, in two or three dimensions, in an arbitrary external potential. Some of our results are analogous to relations derived previously for two-component fermions, and involve derivatives of the energy with respect to the two-body s-wave scattering length a. Moreover, in the three-dimensional case, where the Efimov effect takes place, the interactions are characterized not only by a, but also by a… 

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