Effects of boundaries and density inhomogeneity on states of vortex matter in Bose--Einstein condensates at finite temperature

Most of the literature on quantum vortices predicting various states of vortex matter in three dimensions at finite temperatures in quantum fluids is based on an assumption of an extended and homogeneous system. It is well known not to be the case in actual Bose--Einstein condensates in traps which are finite systems with nonuniform density. This raises the question to what extent one can speak of different aggregate states of vortex matter (vortex lattices, liquids and tensionless vortex tangle) in these system. To address this point, in the present work we focus on the finite-size, boundaries and density inhomogeneity effects on thermal vortex matter in a Bose--Einstein condensate. To this end we perform Monte Carlo simulations on a model system describing trapped Bose--Einstein condensates. Throughout the paper, we draw on analogies with results for vortex matter obtained for extended systems. This work suggests that finiteness and intrinsic inhomogeneity of the system not withstanding, one nonetheless can approximately invoke the notion of distinct aggregate states of vortex matter realized at certain length scales. This might be helpful, in particular in search of possible new states of vortex matter in Bose--Einstein condensates with multiple components and different symmetries.