Do two-dimensional Fermi liquids show odd-even tomographic relaxation
In plain words
In two dimensions, theory predicts that distortions of the electrons' momentum distribution with odd symmetry decay much more slowly than even ones. This would give a distinct transport regime between ballistic and viscous flow.
Precise statement
For a 2D Fermi liquid with $T \ll E_{F}$, kinetic theory dominated by head-on collisions predicts that the slowest odd angular harmonics of the distribution relax at rates $\gamma_{\mathrm{odd}} \sim T^{4}$ (up to logarithms), much smaller than the even rates $\gamma_{\mathrm{even}} \sim T^{2}$ (Ledwith, Guo, Levitov 2019). Is this odd-even effect present in real 2D electron systems, and does it produce the predicted scale-dependent viscosity? Answer yes or no, with measured $\gamma_{\mathrm{odd}}/\gamma_{\mathrm{even}}\ \text{versus}\ T$.
What would settle it
Separate measurement of odd and even harmonic relaxation rates (high-order cyclotron resonance or flow imaging in channels of varying width) showing the predicted temperature dependence.
Status in the literature
Unverified note
Theory (Nilsson, Gran, Hofmann, PRX 2025) finds only a few long-lived odd-parity modes, persisting to $T = 0.15 T_{\mathrm{F}}$; no direct measurement of $\gamma_{\mathrm{odd}}/\gamma_{\mathrm{even}}$ versus $T$ is established.