Generalized Hamiltonian dynamics for vortices in two-dimensional spin systems

Hiroshi Kuratsuji

Using the functional integral for many-boson systems, we propose a new formulation of quantum vortices in two-dimensional superfluids. The motion of vortices is described by a generalized Hamiltonian dynamics in which the equation of motion is governed by a deformed canonical structure. The quantum correspondence of this unusual feature is realized by the anomalous commutators for vortex coordinates. In terms of a semiclassical language, this anomaly yields a consequence that vortex quanta behave like ``anyons.''

John Schliemann, Franz G. Mertens

V. P. Ruban

The dynamics of interacting quantum vortices in a quasi-two-dimensional spatially inhomogeneous Bose–Einstein condensate, whose equilibrium density vanishes at two points of the plane with a possible presence of an immobile vortex with a few circulation quanta at each point, has been considered in a hydrodynamic approximation. A special class of density profiles has been chosen, so that it proves possible to calculate analytically the velocity field produced by point vortices. The equations of motion have been given in a noncanonical Hamiltonian form. The theory has been generalized to the case where the condensate forms a curved quasi-two-dimensional shell in the three-dimensional space.

Richard J. Creswick, Harry L. Morrison

Anderson V. Murray, Andrew J. Groszek, Pekko Kuopanportti +1 more

We have studied numerically the Hamiltonian dynamics of two same-sign point vortices in an effectively two-dimensional, harmonically trapped Bose-Einstein condensate. We have found in the phase space of the system an impenetrable wall that divides the dynamics into two distinct and exhaustive types. In the two-dimensional position-coordinate space, the first type corresponds to intersecting single-vortex orbits and the second type to orbits that have no points in common. The two types are also easily distinguished in the two-dimensional space spanned by the radial and angular velocities of the vortices: In the first type, both single-vortex orbits are the same simple loop in this two-dimensional space, whereas in the second type the two orbits constitute two nonintersecting loops. The phase-space-dividing wall is distinct from the bifurcation curve of rigidly rotating states found by Navarro et al. [Phys. Rev. Lett. 110, 225301 (2013)].

M. S. Makivić, Mark Jarrell