The spatial formation of coherent random laser modes in strongly scattering
disordered random media is a central feature in the understanding of the
physics of random lasers. We derive a quantum field theoretical method for
random lasing in disordered samples of complex amplifying Mie resonators which
is able to provide self-consistently and free of any fit parameter the full set
of transport characteristics at and above the laser phase transition. The
coherence length and the correlation volume respectively is derived as an
experimentally measurable scale of the phase transition at the laser threshold.
We find that the process of stimulated emission in extended disordered
arrangements of active Mie resonators is ultimately connected to time-reversal
symmetric multiple scattering in the sense of photonic transport while the
diffusion coefficient is finite. A power law is found for the random laser mode
diameters in stationary state with increasing pump intensity.Comment: accepted for publication Appl.Sci.(2019), 15 page
