Adapt the framework to chiral superfluids with gapless edges

Develop the detailed adaptation of the odd-viscosity measurement framework to chiral superfluids and superconductors, specifically accounting for the role of gapless edge modes in a bounded sample.

Background

The paper identifies thin films of 3^3He-A and candidate px+ipyp_x+ip_y superconductors as systems in which odd viscosity arises from spontaneous time-reversal breaking and is tied to the orbital spin of Cooper pairs. It argues that the proposed mathscrPTmathscr{PT}-symmetry-based trapped-probe and wave protocols should apply to these systems, with the odd viscosity having an intrinsic quantum origin.

The unresolved issue is the detailed implementation of these protocols in bounded chiral-superfluid or superconducting samples, where gapless edge modes may affect the hydrodynamic response and the interpretation of measurements. The paper explicitly defers this adaptation to future work.

References

We leave the detailed adaptation---in particular the role of the gapless edge in a bounded sample ---to future work.

— $\mathscr{PT}$-symmetric hydrodynamics of odd viscous liquids and their oscillator counterparts  (2608.22958 - Kirkinis et al., 24 Aug 2026) in Section 5.5, “Chiral superfluids and superconductors”