On Effective Theory of Superfluid Phonons

Understand

It is shown that the standard effective field theory of non-relativistic superfluids, which includes only the leading order action in derivative expansion, is in general inadequate for studying supersonic processes.

• Namely, for a proper treatment of the latter the phonons with momenta greater than $mc_s$ are relevant at times (with $m$ being the mass of the superfluid constituent and $c_s$ denoting the sound-speed), which lie beyond the regime of validity of the naive effective theory mentioned above.
• This is demonstrated on a concrete example by recovering the known expression for the friction force as a process of radiating phonons by a supersonic perturber.
• In particular, when the impurity is heavier than superfluid constituents, it is indeed necessary to extend the non-relativistic effective theory of superfluids to include high-derivative corrections.