The role of anyonic excitations in fast rotating harmonically trapped Bose
gases in a fractional Quantum Hall State is examined. Standard Chern-Simons
anyons as well as "non standard" anyons obtained from a statistical interaction
having Maxwell-Chern-Simons dynamics and suitable non minimal coupling to
matter are considered. Their respective ability to stabilize attractive Bose
gases under fast rotation in the thermodynamical limit is studied. Stability
can be obtained for standard anyons while for non standard anyons, stability
requires that the range of the corresponding statistical interaction does not
exceed the typical wavelength for the atoms.Comment: 6 pages. Presented at the "School on Quantum Phase Transitions and
Non-Equilibrium Phenomena in Cold Atomic Gases", ICTP Trieste, 11-22 july
200