Equation of state and contacts of the unitary Bose gas
In plain words
A Bose gas tuned to infinitely strong pair interaction should behave in a universal way, but three-atom collisions destroy it quickly. The question is what state the gas reaches before it decays and what its energy is.
Precise statement
Homogeneous single-species Bose gas quenched to $1/a = 0$ at density n. Determine the quasi-steady energy per particle in units of $E_{n} = \hbar^{2} n^{2/3}/m$, the two-body contact $C_{2}$ and three-body contact $C_{3}$, and their log-periodic dependence on n through the three-body parameter. Answer: values with errors, or proof that no quasi-equilibrium exists on time scales shorter than three-body loss.
What would settle it
Box-trap quench experiments measuring momentum distributions and contacts over several decades of density, compared with many-body theory including three-body physics.
Status in the literature
Quench experiments (JILA 2014; Cambridge, Eigen et al., Nature 2018) observed universal prethermal dynamics, and Ramsey interferometry measured $C_2$ and a first $C_3$ (Fletcher et al., Science 2017); the quasi-steady energy per particle and the log-periodic dependence of $C_3 \text{ on } n$ remain undetermined.