Universal scaling in a trapped Fermi super-fluid in the BCS-unitarity crossover

TL;DR

This paper demonstrates a universal scaling law in a trapped Fermi super-fluid across the BCS-unitarity crossover, enabling predictions of large-system properties from small-system data using numerical density-functional simulations.

Contribution

It introduces a robust scaling approach that links small and large fermion systems in the BCS-unitarity crossover regime, validated through numerical simulations.

Findings

Scaling holds over many orders of magnitude in observables.

Static properties of large systems can be predicted from small system data.

Numerical simulations confirm the universality of the scaling law.

Abstract

Using numerical simulation based on a density-functional equation for a trapped Fermi super-fluid valid along the BCS-unitarity crossover, we establish robust scaling over many orders of magnitude in the observables of the system as a function of fermion number. This scaling allows to predict the static properties of the system, such as energy, chemical potential, etc., for a large number of fermions, over the crossover, from the knowledge of those for a small number ($\sim 4-10$) of fermions.