Critical behavior of second-sound damping at the superfluid transition
In plain words
In a superfluid, heat travels as a wave (second sound). Near the transition its damping should grow following a universal law that has not been measured.
Precise statement
At the unitary superfluid transition (3D XY static class), dynamic scaling predicts divergence of the thermal conductivity and second-sound diffusivity $D_{2}$ near $T_{c}$ with exponents set by the dynamic universality class (model F of Hohenberg-Halperin). Measure $D_{2}(T)$ for $\left|T - T_{c}\right|/T_{c}$ from 0.3 to 0.01 and extract the exponent. Answer: exponent with error and the class it identifies.
What would settle it
Uniform-box second-sound spectroscopy with temperature resolution of order 1% of $T_c$ near the transition.
Status in the literature
Unverified note
Second-sound attenuation was measured through $T_{c}$ in uniform gases (Li et al., Science 2022), and thermography resolved a peak in second-sound diffusivity at $T_{c}$ (Yan et al., Science 2024); no critical exponent has been extracted.