A stone falls into a pond, and ripples spread across the water. Long waves and short ones travel at the same speed: that's how ordinary sound behaves in almost any medium. But in quantum liquids, things can be different.

Physicists considered a superfluid where particles move along a "flat" energy band. It's like a highway without hills or dips: speed doesn't change, energy stays constant. In such a medium, collective oscillations, ripples in density and pairing, merge into a single unusual wave. Its frequency grows not linearly with wavelength but quadratically. Long waves become very slow, almost frozen. The discovery links quantum geometry, the internal "curvature" of states, with macroscopic motion.

The coefficient of the quadratic term depends on the "quantum metric." This mathematical object describes how strongly states in the flat band "feel" each other at a distance. It's like a spring: its stiffness determines the oscillation frequency of a mass. The calculations were confirmed by numerical simulations. The result applies to any s-wave superfluid system with an isolated flat band — from ultracold atoms to exotic layered materials.

A stone thrown into such a pond would produce not ripples but a slowly spreading patch. As if the water became thicker only for long waves.