If dark matter in the galactic halo is composed of bosons that form a Bose-Einstein condensate then it is likely that the rotation of the halo will lead to the nucleation of vortices. After a review of the Gross-Pitaevskii equation, the Thomas-Fermi approximation and vortices in general, we consider vortices in detail. We find strong bounds for the boson mass, interaction strength, the shape and quantity of vortices in the halo, the critical rotational velocity for the nucleation of vortices and, in the Thomas-Fermi regime, an exact solution for the mass density of a single, axisymmetric vortex.PACS numbers: 05.30.Jp, 95.35.+d

No abstract

We consider a polaronic model in which impurity fermions interact with background bosons in a dipolar condensate. The polaron in this model emerges as an impurity dressed with a cloud of phonons of the dipolar condensate, which, due to the competition between the attractive and repulsive parts of the dipole-dipole interaction, obey an anisotropic dispersion spectrum. We study how this anisotropy affects theČerenkov-like emission of Bogoliubov phonon modes, which can be directly verified by experiments in which a dipolar Bose-Einstein condensate moves against an obstacle. We also study the spectral function of impurity fermions, which is directly accessible to the momentum-resolved rf spectroscopy in cold atoms.

Yin and Radzihovsky [1] recently developed a self-consistent extension of a Bogoliubov theory, in which the condensate number density nc is treated as a mean field that changes with time, in order to analyze a JILA experiment by Makotyn et al.[2] on a 85 Rb Bose gas following a deep quench to a large scattering length. We apply this theory to construct a closed set of equations that highlight the role ofṅc, which is to induce an effective interaction between quasiparticles. We show analytically that such a system supports a steady state characterized by a constant condensate density and a steady but periodically changing momentum distribution, whose time average is described exactly by the generalized Gibbs ensemble. We discuss how theṅc-induced effective interaction, which cannot be ignored on the grounds of the adiabatic approximation for modes near the gapless Goldstone mode, can significantly affect condensate populations and Tan's contact for a Bose gas that has undergone a deep quench.

We adapt the generalized Hartree-Fock-Bogoliubov (HFB) method to an interacting many-phonon system free of impurities. The many-phonon system is obtained from applying the Lee-Low-Pine (LLP) transformation to the Fröhlich model which describes a mobile impurity coupled to noninteracting phonons. We specialize our general HFB description of the Fröhlich polaron to Bose polarons in quasi-1D cold atom mixtures. The LLP transformed many-phonon system distinguishes itself with an artificial phonon-phonon interaction which is very different from the usual two-body interaction. We use the quasi-one-dimensional model, which is free of an ultraviolet divergence that exists in higher dimensions, to better understand how this unique interaction affects polaron states and how the density and pair correlations inherent to the HFB method conspire to create a polaron ground state with an energy in good agreement with and far closer to the prediction from Feynman's variational path integral approach than mean-field theory where HFB correlations are absent.

I derive a system of pulsation equations for compact stars made up of an arbitrary number of perfect fluids that can be used to study radial oscillations and stability with respect to small perturbations. I assume spherical symmetry and that the only inter-fluid interactions are gravitational. My derivation is in line with Chandrasekhar's original derivation for the pulsation equation of a single-fluid compact star and keeps the contributions from the individual fluids manifest. I illustrate solutions to the system of pulsations equations with one-, two-, and three-fluid examples.

We consider the growth of cosmological perturbations to the energy density of dark matter during matter domination when dark matter is a scalar field that has undergone Bose-Einstein condensation. We study these inhomogeneities within the framework of both Newtonian gravity, where the calculation and results are more transparent, and General Relativity. The direction we take is to derive analytical expressions, which can be obtained in the small pressure limit. Throughout we compare our results to those of the standard cosmology, where dark matter is assumed pressureless, using our analytical expressions to showcase precise differences. We find, compared to the standard cosmology, that Bose-Einstein condensate dark matter leads to a scale factor, gravitational potential and density contrast that increase at faster rates.PACS numbers: 05.30.Jp, 95.35.+d

recently made a renormalization group study of a one-dimensional Bose polaron in cold atoms. Their study went beyond the usual Fröhlich description, which includes only single-phonon processes, by including two-phonon processes in which two phonons are simultaneously absorbed or emitted during impurity scattering [Shchadilova et. al., Phys. Rev. Lett. 117, 113002 (2016)]. We study this same beyond-Fröhlich model, but in the static impurity limit where the ground state is described by a multimode squeezed state instead of the multimode coherent state in the static Fröhlich model. We solve the system exactly by applying the generalized Bogoliubov transformation, an approach that can be straightforwardly adapted to higher dimensions. Using our exact solution, we obtain a polaron energy free of infrared divergences and construct analytically the polaron phase diagram. We find that the repulsive polaron is stable on the positive side of the impurity-boson interaction but is always thermodynamically unstable on the negative side of the impurity-boson interaction, featuring a bound state, whose binding energy we obtain analytically. We find that the attractive polaron is always dynamically unstable, featuring a pair of imaginary energies which we obtain analytically. We expect the multimode squeezed state to help with studies that go not only beyond the Fröhlich paradigm but also beyond Bogoliubov theory, just as the multimode coherent state has helped with the study of Fröhlich polarons.