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Sound attenuation in a free fermi gas

Physics Asked on June 21, 2021

In Feynman’s book on statistical mechanics, he stated that sound cannot propagate in a collisionless electron gas. It is on page 245. I do not fully understand his argument. We know that the velocity of sound in a media is given by the formula

$$ v = sqrt{K_s/rho} ,$$

where $K_s$ is the bulk modulus and $rho$ is the mass density. It seems that as long as the media has a positive bulk modulus (a free fermi gas definitely belongs to this category), it can support sound propagation. So, what is the extra condition for sound propagation? If a free fermi gas cannot support sound, what is its response to a local kick?

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