An impurity immersed in a Bose-Einstein condensate is no longer accurately described by the Fröhlich Hamiltonian as the coupling between the impurity and the boson bath gets stronger. We study the dominant effects of the twophonon terms beyond the Fröhlich model on the ground state properties of the polaron using Feynman's variational path-integral approach. The previously reported discrepancy in the effective mass between the renormalization group approach and this theory is shown to be absent in the beyond-Fröhlich model on the positive side of the Feshbach resonance. Self-trapping, characterized by a sharp and dramatic increase of the effective mass, is no longer observed for the repulsive polaron once the two-phonon interactions are included. For the attractive polaron we find a divergence of the ground state energy and effective mass at weaker couplings than previously observed within the Fröhlich model. * timour.ichmoukhamedov@uantwerpen.be arXiv:1905.07368v1 [cond-mat.quant-gas]

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Dilute ultracold quantum gases form an ideal and highly tunable system in which superfluidity can be studied. Recently quantum turbulence in Bose-Einstein condensates was reported [PRL 103, 045310 (2009)], opening up a new experimental system that can be used to study quantum turbulence. A novel feature of this system is that vortex cores now have a finite size. This means that the vortices are no longer one dimensional features in the condensate, but that the radial behaviour and excitations might also play an important role in the study of quantum turbulence in Bose-Einstein condensates. In this paper we investigate these radial modes using a simplified variational model for the vortex core. This study results in the frequencies of the radial modes, which can be compared with the frequencies of the thoroughly studied Kelvin modes. From this comparison we find that the lowest (l=0) radial mode has a frequency in the same order of magnitude as the Kelvin modes. However the radial modes still have a larger energy than the Kelvin modes, meaning that the Kelvin modes will still constitute the preferred channel for energy decay in quantum turbulence. a e-mail: nick.verhelst@uantwerpen.be arXiv:1707.08382v1 [cond-mat.quant-gas]

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