Fractional quantum mechanics in polariton condensates with velocity dependent mass

We introduce and analyze a novel mean-field model for polariton condensates with velocity dependence of the effective polariton mass due the photon and exciton components. The effective mass depends on the in-plane wave vector k, which at the inflection point of the lower polariton energy branch becomes infinite and above negative. The polariton condensate modes of the new mean-field theory are now sensitive to mass variations and for certain points of the energy dispersion the polariton condensate mode represents fractional quantum mechanics. The impact of the generalized kinetic energy term is elucidated by numerical studies in 1D and 2D showing significant differences for large velocities. Analytical expressions for plane wave solutions as well as a linear waves analysis show the significance of this new model.