Thermal fluctuations of vortex clusters in quasi-two-dimensional   Bose-Einstein condensate
  We study the thermal fluctuations of vortex positions in small vortex clusters in a harmonically trapped rotating Bose-Einstein condensate. It is shown that the order-disorder transition of two-shells clusters occurs via the decoupling of shells with respect to each other. The corresponding "melting" temperature depends stronly on the commensurability between numbers of vortices in shells. We show that "melting" can be achieved at experimentally attainable parameters and very low temperatures. Also studied is the effect of thermal fluctuations on vortices in an anisotropic trap with small quadrupole deformation. We show that thermal fluctuations lead to the decoupling of a vortex cluster from the pinning potential produced by this deformation. The decoupling temperatures are estimated and strong commensurability effects are revealed. 
W. V. Pogosov and K. Machida