Vortex pair annihilation in arrays of photon cavities

We investigate theoretically the evolution of the vortex number in an array of photon condensates that is brought from an incoherent low density state to a coherent high density state by a sudden change in the pumping laser intensity. We analyze how the recombination of vortices and antivortices depends on the system parameters such as the coefficients for emission and absorption of photons by the dye molecules, the rate of tunneling between the cavities, the photon loss rate and the number of photons in the condensate.