2010/12/01 by Vı́ctor Romero-Rochı́n, Romero-Rochin, Victor
Physics and Astronomy · #Atomic and Subatomic Physics Research #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Gases (cond-mat.quant-gas) #Quantum, superfluid, helium dynamics
paper · pdf · doi:10.48550/arxiv.1012.0236
openalex publication_date 2010/12/01 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
As can be inferred from present experiments in ultracold gases, the\nscattering length is a quantity that determines the thermodynamic state of the\ngas. As such, there exists a conjugate thermodynamic to it. Here, we show that\nthe recently introduced "contact" is the conjugate of the inverse of the\nscattering length. We find that this identification allows for a derivation of\nessentially all the known results regarding the contact. Using the mean-field\ntheory for the Bose-Einstein (BEC) to Bardeen-Cooper-Schriefer (BCS) crossover,\nwe also find that the contact is proportional to the square of the gap. We\nanalyze in detail both a homogenous balanced mixture of fermions and its\ninhomogenous counterpart in a harmonic trap.\n