Effective field theory and dispersion law of the phonons of a non-relativistic superfluid

Abstract

We study the recently proposed effective field theory for the phonon of an arbitrary non-relativistic superfluid. After computing the one-loop phonon self-energy, we obtain the low temperature T contributions to the phonon dispersion law at low momentum, and see that the real part of those can be parametrized as a thermal correction to the phonon velocity. Because the phonons are the quanta of the sound waves, at low momentum their velocity should agree with the speed of sound. We find that our results match at order T^4ln(T) with those predicted by Andreev and Khalatnikov for the speed of sound, derived from the superfluid hydrodynamical equations and the phonon kinetic theory. We get also higher order corrections of order T^4, which are not reproduced pushing naively the kinetic theory computation. Finally, as an application, we consider the cold Fermi gas in the unitarity limit, and find a universal expression for the low T relative correction to the speed of sound for these systems.

14 pages, 2 figures. References added

References in corpus (8)

• Theory of ultracold Fermi gases
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Universal properties of a trapped two-component Fermi gas at unitarity
• Shear viscosity of a superfluid Fermi gas in the unitarity limit
• Density Functional Theory for non-relativistic Fermions in the Unitarity Limit
• Bulk viscosities for cold Fermi superfluids close to the unitary limit
• Effective theory for the Goldstone field in the BCS-BEC crossover at T=0

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• Thermal conductivity due to phonons in the core of superfluid neutron stars
• Collective modes in the color flavor locked phase
• Phonon contribution to the shear viscosity of a superfluid Fermi gas in the unitarity limit
• Bulk viscosity coefficients due to phonons in superfluid neutron stars
• Superfluid Effective Field Theory for Dark Matter Direct Detection
• Transport properties of superfluid phonons in neutron stars
• Phonon damping in a 2D superfluid: insufficiency of Fermi's golden rule at low temperature
• Mechanism of collisionless sound damping in dilute Bose gas with condensate
• Photonic Nambu-Goldstone bosons