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Most of the literature on quantum vortices predicting various states ofvortex matter in three dimensions at finite temperatures in quantum fluids isbased on an assumption of an extended and homogeneous system. It is well knownnot to be the case in actual Bose--Einstein condensates in traps which arefinite systems with nonuniform density. This raises the question to what extentone 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 densityinhomogeneity effects on thermal vortex matter in a Bose--Einstein condensate.To this end we perform Monte Carlo simulations on a model system describingtrapped Bose--Einstein condensates. Throughout the paper, we draw on analogieswith results for vortex matter obtained for extended systems. This worksuggests that finiteness and intrinsic inhomogeneity of the system notwithstanding, one nonetheless can approximately invoke the notion of distinctaggregate states of vortex matter realized at certain length scales. This mightbe helpful, in particular in search of possible new states of vortex matter inBose--Einstein condensates with multiple components and different symmetries.

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