Vortex formation in a two-dimensional Bose gas

ESTEBAN CALZETTA; KWAN-YUET HO; BEI-LOK HU

JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS

IOP PUBLISHING LTD

Lugar: Londres; Año: 2010 vol. 43 p. 95004 - 95004

0953-4075

We discuss the stability of a homogeneous two-dimensional Bose gas at finite temperatureagainst the formation of isolated vortices. We consider a patch of several healing lengths insize and compute its free energy using the Euclidean formalism. Since we deal with an opensystem, which is able to exchange particles and angular momentum with the rest of thecondensate, we use the symmetry-breaking (as opposed to the particle number conserving)formalism, and include configurations with all values of angular momenta in the partitionfunction. At finite temperature, there appear sphaleron configurations associated with isolatedvortices. The contribution from these configurations to the free energy is computed in thedilute gas approximation. We show that the Euclidean action of linearized perturbations of avortex is not positive definite. As a consequence the free energy of the 2D Bose gas acquiresan imaginary part. This signals the instability of the gas. This instability may be identifiedwith the Berezinskii–Kosterlitz–Thouless transition.