= First-to-zero-sound crossover
{title2=$\omega\tau$}
Angular-relaxation collision time $\tau$ distinguishes <first sound> ($\omega\tau\ll1$) from <zero sound> ($\omega\tau\gg1$). Collisions establish local <thermodynamic equilibrium> in the former.<Oscillations in a Fermi Liquid by Lev Davidovich Landau>[Sections 2–3, finite-temperature kinetic equation and absorption]{ref}
For the figure's stipulated law $\omega\tau=(T/T_\times)^{-2}$, cooling from $T=5T_\times$ to $T=T_\times/5$ changes $\omega\tau$ from $0.04$ to $25$, without changing the driving <angular frequency>. The crossover temperature is defined by $\omega\tau(T_\times)=1$. Calling <zero sound> a high-frequency mode therefore means high relative to the collision rate $1/\tau$, while its excitation <energy> must still remain within the low-energy domain of the <Fermi liquid>.
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