Collective excitations of composite fermions across multiple effective Landau levels

The paradigm of density-wave modulation over the ground state
as collective excitations, pioneered by Feynman, works very well
for fundamentally important excitations from the roton in superfluid Helium-4 to the plasmon in electron gas. This approximation which is basically a single mode approximation predicts experimentally observed rotons in the collective
excitations of fractional quantum Hall states as well. However, this theory fails to explain the recent observation of merging of modes in the long wave length limit at fractional quantum Hall state 1/3 by inelastic light scattering experiments. In this talk, I will present our theory which solves this puzzle and predicts several other experimentally verifiable features some of which are already observed.