Thermal Fluctuations of Vortex Matter in Trapped Bose-Einstein Condensates

We perform Monte Carlo studies of vortices in three dimensions in a cylindrical confinement, with uniform and nonuniform density. The former is relevant to rotating 4He, the latter is relevant to a rotating trapped Bose--Einstein condensate. In the former case we find dominant angular thermal vortex fluctuations close to the cylinder wall. For the latter case, a novel effect is that at low temperatures the vortex solid close to the center of the trap crosses directly over to a tension-less vortex tangle near the edge of the trap. At higher temperatures an intermediate tensionful vortex liquid located between the vortex solid and the vortex tangle, may exist.