Mutual Interactions of Phonons, Rotons, and Gravity
Alberto Nicolisa and Riccardo Pencob
a Center for Theoretical Physics and Department of Physics, Columbia University, New York, NY 10027, USA b Center for Particle Cosmology, Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
Abstract We introduce an effective point-particle action for generic particles living in a zero- temperature superfluid. This action describes the motion of the particles in the medium at equilibrium as well as their couplings to sound waves and generic fluid flows. While we place the emphasis on elementary excitations such as phonons and rotons, our formalism applies also to macroscopic objects such as vortex rings and rigid bodies interacting with long-wavelength fluid modes. Within our approach, we reproduce phonon decay and phonon-phonon scattering as predicted using a purely field-theoretic description of phonons. We also correct classic results by Landau and Khalatnikov on roton-phonon scattering. Finally, we discuss how phonons and rotons couple to gravity, and show that the former tend to float while the latter tend to sink but with rather peculiar trajectories. Our formalism can be easily extended to include (general) relativistic effects and couplings to additional matter fields. As such, it can be relevant in contexts as diverse as neutron star physics and light dark matter detection.
1 Introduction
Neutron scattering experiments [1] show that the spectrum of elementary excitations in su- perfluid helium-4 at very low temperatures looks schematically as in Figure 1. A similar dispersion relation was also observed numerically [2] as well as experimentally [3] in trapped gases made of weakly interacting dipolar particles. There are two regions of momenta where the corresponding excitations are always kinematically stable1: one is around p = 0, the arXiv:1705.08914v1 [hep-th] 24 May 2017 other is around p = p∗. Excitations in these regions are usually treated as different species of particles and are referred to as phonons and rotons respectively. Phenomenologically, their dispersion relations can be extracted by Taylor expanding the experimental dispersion curve around p = 0 and p = p∗ to obtain
2 (p − p∗) Ephonon ' csp , Eroton ' ∆ + . (1) 2m∗
1Depending on the precise shape of the dispersion curve, excitations in the region surrounding the local maximum could also be kinematically stable. Such excitations are usually referred to as maxons. The formalism that we will here can be applied to maxons as well.
1 E