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arXiv:hep-th/0608216 · Annals of Physics

Fractionalization of angular momentum at finite temperature around a magnetic vortex

Yu.A. Sitenko, N.D. Vlasii

Published Mar 4, 2007• 1 citation
arXivHTMLPDF
DOI
10.1016/j.aop.2006.05.006

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Ambiguities in the definition of angular momentum of a quantum-mechanical particle in the presence of a magnetic vortex are reviewed. We show that the long-standing problem of the adequate definition is resolved in the framework of the second-quantized theory at nonzero temperature. Planar relativistic Fermi gas in the background of a point-like magnetic vortex with arbitrary flux is considered, and we find thermal averages, quadratic fluctuations, and correlations of all observables, including angular momentum, in this system. The kinetic definition of angular momentum is picked out unambiguously by the requirement of plausible behaviour for the angular momentum fluctuation and its correlation with fermion number.
Though vortices are an unavoidable presence in bulk superfluid helium, they have not been observed to date in helium nanodroplets. The energy and angular momentum of both straight and curved vortex states of a helium nanodroplet are examined as a function of droplet size. For droplets in the size range of many experiments, it is found that during the pickup of heavy solutes, a significant fraction of events deposit sufficient energy and angular momentum to form a straight vortex line. Curved vortex lines exist down to nearly zero angular momentum and energy, and thus could in principle form in almost any collision. Further, the coalescence of smaller droplets during the cooling by expansion could also deposit sufficient angular momentum to form vortex lines. Despite their high energy, most vortices are predicted to be stable at the final temperature (0.38 K) of helium nanodroplets due to lack of decay channels that conserve both energy and angular momentum.
We perform finite-temperature dynamical simulations of the arrest of a rotating Bose-Einstein condensate by a fixed trap anisotropy, using a Hamiltonian classical-field method. We consider a quasi-two-dimensional condensate containing a single vortex in equilibrium with a rotating thermal cloud. Introducing an elliptical deformation of the trapping potential leads to the loss of angular momentum from the system. We identify the condensate and the complementary thermal component of the nonequilibrium field and compare the evolution of their angular momenta and angular velocities. By varying the trap anisotropy we alter the relative efficiencies of the vortex-cloud and cloud-trap coupling. For strong trap anisotropies the angular momentum of the thermal cloud may be entirely depleted before the vortex begins to decay. For weak trap anisotropies, the thermal cloud exhibits a long-lived steady state in which it rotates at an intermediate angular velocity.