Anyonic Excitations in Fast Rotating Bose Gases

6 pages. Presented at the \"School on Quantum Phase Transitions and Non-Equilibrium Phenomena in Cold Atomic Gases\", ICTP Trieste, 11-22 july 2005The 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