van der Waals Universality near a Quantum Tricritical Point

We study the three-body scattering hypervolume D of atoms whose scattering length a is on the order of or smaller than the typical range r(vdW) of the van derWaals attraction. We find that the real part of D behaves universally in this weakly interacting regime (vertical bar a vertical bar/r(vdW) less than or similar to 1) in the absence of trimer resonances. This universality originates from hard-spherelike collisions that dominate elastic three-body scattering. We use this result to make quantitative predictions for the thermodynamics and elementary excitations of an atomic Bose-Einstein condensate in the vicinity of a quantum tricritical point, including quantum droplets stabilized by effective three-body interactions.