Self-duality and long-wavelength behavior of the Landau-level guiding-center structure function, and the shear modulus of fractional quantum Hall fluids

A remarkable self-duality of the “guiding-center” structure function s(q) of particles in a partially-filled 2D Landau level is used to express the long-wavelength collective excitation energy of fractional quantum Hall fluids in terms of a shear modulus. A bound on the small-q behavior of s(q) is given.