vix.ing · top · new · best · stats · spec

The Unitary Gas and its Symmetry Properties

2011/03/31 by Yvan Castin, Félix Werner · 1 citation
Physics and Astronomy · #Atomic and Subatomic Physics Research #Cold Atom Physics and Bose-Einstein Condensates #Crossover #Fermion #Feshbach resonance #Geometry #Isotropy #Molecule #Momentum (technical analysis) #Physics #Quantum mechanics #Quantum, superfluid, helium dynamics #Scaling #Symmetry (geometry) #Unitary state #cond-mat.quant-gas

paper · pdf · doi:10.1007/978-3-642-21978-8_5

63 pages, 8 figures. Contribution to the Springer Lecture Notes in Physics "BEC-BCS Crossover and the Unitary Fermi gas" edited by Wilhelm Zwerger. Revised version correcting a few typos

arxiv created 2011/09/14 · openalex publication_date 2011/10/19 · arxiv updated 2015/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The physics of atomic quantum gases is currently taking advantage of a powerful tool, the possibility to fully adjust the interaction strength between atoms using a magnetically controlled Feshbach resonance. For fermions with two internal states, formally two opposite spin states, this allows to prepare long lived strongly interacting three-dimensional gases and to study the BEC-BCS crossover. Of particular interest along the BEC-BCS crossover is the so-called unitary gas, where the atomic interaction potential between the opposite spin states has virtually an infinite scattering length and a zero range. This unitary gas is the main subject of the present chapter: It has fascinating symmetry properties, from a simple scaling invariance, to a more subtle dynamical symmetry in an isotropic harmonic trap, which is linked to a separability of the N-body problem in hyperspherical coordinates. Other analytical results, valid over the whole BEC-BCS crossover, are presented, establishing a connection between three recently measured quantities, the tail of the momentum distribution, the short range part of the pair distribution function and the mean number of closed channel molecules.

Citations

Cited by