I have a new preprint out, where I study the large-\(N\) scaling of Tan’s contact for the harmonically trapped Tonks–Girardeau gas at finite temperature.

Abstract

We examine the canonical-ensemble scaling of Tan’s contact for \(N\) harmonically trapped Tonks–Girardeau bosons at finite temperature. The leading scaling coefficient aligns with local-density-approximation findings, and is derived through a contour-integral representation and a saddle-point reduction. The subleading coefficient is expressed through universal phase-space integrals of the Fermi factor, with closed-form Sommerfeld and virial limits. We provide Padé approximants interpolating between the low- and high-temperature regimes, and validate the results using canonical contour-integration across all temperatures examined.

Check it out arxiv:2605.15994.

Enjoy!