Phonon damping in a 2D superfluid: insufficiency of Fermi's golden rule at low temperature

Abstract

It is generally accepted that the phonon gas of a superfluid always enters a weak coupling regime at sufficiently low temperatures, whatever the strength of the interactions between the underlying particles (constitutive of the superfluid). Thus, in this limit, we should always be able to calculate the damping rate of thermal phonons by applying Fermi's golden rule to the Hamiltonian $H_3$ of cubic phonon-phonon coupling taken from quantum hydrodynamics, at least in the case of a convex acoustic branch and in the collisionless regime (where the eigenfrequency of the considered phonons remains much greater than the gas thermalization rate). Using the many-body Green's function method, we predict that, unexpectedly, this is not true in two dimensions, contrary to the three-dimensional case. We confirm this prediction with classical phonon-field simulations and a non-perturbative theory in $H_3$, where the fourth order is regularized by hand, giving a complex energy to the virtual phonons of the four-phonon collisional processes. For a weakly interacting fluid and a phonon mode in the long-wavelength limit, we predict a damping rate about three times lower than that of the golden rule.

In French (43 pages) and in English (42 pages) (published version)

References in corpus (6)

• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Bragg spectroscopy of a strongly interacting Fermi gas
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Cited by in corpus (2)

• Comment on "Excitation Spectrum and Superfluid Gap of an Ultracold Fermi Gas"
• Emergence of Fermi's Golden Rule in the Probing of a Quantum Many-Body System