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Fundamental understanding of strongly-interacting systems necessarilyinvolves collective modes, but their nature and evolution is not generallyunderstood in dynamically disordered and strongly-interacting systems such asliquids and supercritical fluids. We report the results of extensive moleculardynamics simulations and provide direct evidence that liquids develop a gap insolid-like transverse spectrum in the reciprocal space, with no propagatingmodes between zero and a threshold value. In addition to the liquid state, thisresult importantly applies to the supercritical state of matter. We show thatthe emerging gap increases with the inverse of liquid relaxation time anddiscuss how the gap affects properties of liquid and supercritical states.

Emergence and evolution of $k$-gap in spectra of liquid and supercritical states