Zero sound is the name given by Landau to the unique quantum vibrations in quantum Fermi liquid

Fermi liquid

Fermi liquid theory is a theoretical model of interacting fermions that describes the normal state of most metals at sufficiently low temperatures. The interaction between the particles of the many-body system does not need to be small...

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This sound can no longer be thought of as a simple wave of compression and rarefaction.

As the shape of Fermi distribution function changes slightly(or largely), zero sound propagates in the direction for the head of Fermi surface with no change of the density of the liquid.