Triviality of Entanglement Entropy in the Galilean Vacuum

We study the entanglement entropy of the vacuum in non-relativistic local theories with Galilean or Schr\"{o}dinger symmetry. We clear some confusion in the literature on the free Schr\"odinger case. We find that with only positive $U(1)$ charge particles (states) and a unique zero $U(1)$ charge state (the vacuum) the entanglement entropy must vanish in that state

Jeans Instability in Superfluids

We analyze the effect of a gravitational field on the sound modes of superfluids. We derive an instability condition that generalizes the well known Jeans instability of the sound mode in normal fluids. We discuss potential experimental implications.Comment: 9 pages, Late

Spontaneous breaking of non-relativistic scale symmetry

Abstract We analyze the mechanism of spontaneous symmetry breaking of scale invariance in Galilean invariant field theories. We show that the existence of a dynamic gapless dilaton mode depends on whether the U(1) particle number or the Galilean boost symmetry are spontaneously broken. When both scale and particle number symmetries are spontaneously broken there is one propagating gapless Nambu-Goldstone mode. Its dispersion relation is linear if the chemical potential is nonzero and quadratic otherwise. We discuss the reversibility of RG flows in such theories