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Bose-Einstein Condensation and Superfluidity$
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Lev Pitaevskii and Sandro Stringari

Print publication date: 2016

Print ISBN-13: 9780198758884

Published to Oxford Scholarship Online: March 2016

DOI: 10.1093/acprof:oso/9780198758884.001.0001

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Tan Relations and the Contact Parameter

Tan Relations and the Contact Parameter

(p.341) 18 Tan Relations and the Contact Parameter
Bose-Einstein Condensation and Superfluidity

Lev Pitaevskii

Sandro Stringari

Oxford University Press

This chapter is devoted to the derivation of various thermodynamic relations, known as Tan relations, involving the so-called contact parameter. This physical quantity, which determines the behaviour of the momentum distribution of an interacting gas at large momenta, plays a crucial role in characterizing various thermodynamic quantities, like the dependence of the energy on the scattering length (sweep theorem), the relation between the energy and the momentum distribution, the behaviour of the static structure factor at large wave vectors, and the virial theorem in the presence of harmonic trapping.

Keywords:   Tan relations, contact parameter, total contact parameter, momentum distribution, sweep theorem, scattering length, energy and momentum distribution, static structure factor, virial theorem

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