# 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}
}
• Published 5 October 2012
• Physics
• Physical Review A
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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## References

SHOWING 1-10 OF 63 REFERENCES
Short Range Scaling Laws of Quantum Gases With Contact Interactions
The probability amplitude for $N$ particles in a quantum gas with negligible range of interparticle interaction potentials to come to a small region of size $r$ scales like $r^\gamma$. It is shown
Table of Integrals, Series, and Products
• Mathematics
• 1943
Introduction. Elementary Functions. Indefinite Integrals of Elementary Functions. Definite Integrals of Elementary Functions. Indefinite Integrals of Special Functions. Definite Integrals of Special
Ann
• Psychology
• 2005
Aaron Beck’s cognitive therapy model has been used repeatedly to treat depression and anxiety. The case presented here is a 34-year-old female law student with an adjustment disorder with mixed
• Fiz. 12, 1080 (1970), [Sov. J. Nucl. Phys. 12, 589
• 1971
Phys
• Rev. A 79, 053640
• 2009
Phys
• Rev. A 86, 013626
• 2012
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
Found
• C. Ross
• Medicine
The Dental register
• 1869
Tables of integrals
• Mathematics
• 1998