COLLECTIVE EXCITATIONS IN THE GINZBURG-LANDAU THEORY OF THE FRACTIONAL QUANTUM HALL-EFFECT

The collective excitations of the fractional-quantum-Hall liquid are studied within the Ginzburg-Landau theory. We show that (1) Gaussian fluctuations of the phase of the order parameter correspond to the cyclotron mode with an energy gap of h-omega-c at q--> = 0 and a contribution to the static structure factor proportional to /q-->/2 as q--> --> 0, in accordance with Kohn's theorem, and (2) vortex-antivortex fluctuations give rise to the lowest-Landau-level collective mode with an energy gap that depends only on the Coulomb energy and a static structure factor that vanishes as /q-->/4 as q--> --> 0.