Joint ICTP/SISSA Statistical Physics Seminar: Tan's Contact for a Strongly Interacting One-dimensional Bose Gas in Harmonic Confinement: Universal Properties and Scaling Functions
Starts 19 Feb 2018 11:00
Ends 19 Feb 2018 12:00
Central European Time
The Tan's contact is an ubiquitous quantity in systems with zero-range interactions: it corresponds for example to the average interaction energy, to the weight of the tails of the momentum distribution function at large momenta, to the inelastic two-body loss rate, just to cite a few. We focus on strongly interacting one-dimensional bosons at finite temperature under harmonic confinement. As it is associated to short-distance correlations, the calculation of the Tan's contact cannot be obtained within the Luttinger-liquid formalism. We derive the Tan's contact by employing an exact solution at infinite interactions, as well as a local-density approximation on the Bethe Ansatz solution for the homogeneous system and numerical ab initio calculations for finite interactions. In the limit of infinite interactions, we demonstrate its universal properties, associated to the scale invariance of the model. We then obtain the full scaling function for arbitrary interactions.