New insights into rotating BECs.
Rotating atomic BECs have been experimentally realizable since 15 years ago ca. However, up to now only little effort has been put to topologically characterize their excitations. The system explicitly breaks parity and time-reversal symmetries and breaks spontaneously rotational invariance via the formation of the vortex lattice. Unlike quantum Hall fluids, the system is compressible. The endeavour is to evaluate transport and edge properties by approaching the problem both by the microscopic (Gross-Pitaevskii) theory and from an effective field theory viewpoint. The Nambu-Goldstone bosons for the low-energy theory are the Tkachenko modes: elliptically polarized vortex-lattice vibrations with soft (quadratic) dispersion. The usual phononic branch is not present since it is redundant to the TK. The system can also be investigated using the dual gauge description using two-dimensional boson-vortex duality.