Anyons and Superconductivity: Random Phase Approximation

The two-dimensional ideal gas of particles obeying ν fractional statistics is recast as an interacting Fermi gas with long-range gauge potentials. A self-consistent dielectric description of the random phase approximation (RPA) provides a concise expression for the linear response of the fractional statistics gas to an external electromagnetic field. The RPA, believed to be correct for the present case of long-range interactions, yields two central results that are classic features of superconductivity: (1) a sharp undamped collective mode with a linear dispersion relation at long wavelengths: (2) a gauge-invariant Meissner effect in the transverse response to an external magnetic field.