http://arxiv.org/abs/1909.05710
Superfluid dark matter postulates that the centers of galaxies contain superfluid condensates. An important quantity regarding these superfluids is their chemical potential $ \mu $. Here, we discuss two issues related to this chemical potential. First, there is no exactly conserved quantity associated with this chemical potential due to the symmetry-breaking baryon-phonon coupling. Second, $ \mu $ is sometimes introduced by shifting the phonon field by $ \mu \cdot t $ which — again due to the symmetry-breaking baryon-phonon coupling — introduces an explicit time dependence in the Lagrangian. We investigate under which conditions introducing a chemical potential is nevertheless justified and show how to correctly introduce it when these conditions are met. We further propose a model that recovers superfluid dark matter’s zero-temperature equations of motion including a chemical potential even if the aforementioned conditions for justifying a chemical potential are not met.
T. Mistele
Fri, 13 Sep 19
6/70
Comments: 20 pages
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