Vortex lattices in Bose-Einstein condensates with dipolar interactions beyond the weak-interaction limit
We study the ground states of rotating atomic Bose-Einstein condensates with dipolar interactions. We present the results of numerical studies on a periodic geometry which show vortex lattice ground states of various symmetries: triangular and square vortex lattices, ``stripe crystal,'' and ``bubble crystal.'' We present the phase diagram (for systems with a large number of vortices) as a function of the ratio of dipolar to contact interactions and of the chemical potential. We discuss the experimental requirements for observing transitions between vortex lattice ground states via dipolar interactions. We finally investigate the stability of mean-field supersolid phases of a quasi-two-dimensional nonrotating Bose gas with dipolar interactions.
Abstract We discuss random matrix-model representations of D = 1 string theory, with particular emphasis on the case in which the target space is a circle of finite radius. The duality properties of discretized strings are analyzed and shown to depend on the dynamics of vortices. In the representation in terms of a continuous circle of matrices we find an exact expression for the free energy, neglecting non-singlet states, as a function of the string coupling and the radius which exhibits exact duality. In a second version, based on a discrete chain of matrices, we find that vortices induce, for a finite radius, a Kosterlitz-Thouless phase transition that takes us to a c = 0 theory.