On Effective Theory of Superfluid Phonons

Abstract

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 $m{c}_s$ 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. For the light perturber, however, there is a window of velocities for which high-derivative corrections are irrelevant.

11 pages

References in corpus (5)

• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Light Dark Matter in Superfluid Helium: Detection with Multi-excitation Production
• Low-Energy Quantum Effective Action for Relativistic Superfluids
• Sub-GeV Dark Matter in Superfluid He-4: an Effective Theory Approach
• Emergent long-range interactions in Bose-Einstein Condensates

Cited by in corpus (8)

• Ultra-Light Dark Matter
• A Holographic Superfluid Symphony
• Optomechanical dark matter instrument for direct detection
• Directional detection of light dark matter from three-phonon events in superfluid ${}^4$He
• Cherenkov radiation from stars constrains hybrid MOND dark matter models
• Finite Temperature Description of an Interacting Bose Gas
• Thermalization, Fragmentation and Tidal Disruption: The Complex Galactic Dynamics of Dark Matter Superfluidity
• Boundary effects on classical liquid density fluctuations