Quantum statistics of overlapping modes in open resonators

We study the quantum dynamics of optical fields in weakly confining resonators with overlapping modes. Employing a recently developed quantization scheme involving a discrete set of resonator modes and continua of external modes we derive Langevin equations and a master equation for the resonator modes. Langevin dynamics and the master equation are proved to be equivalent in the Markovian limit. Our open-resonator dynamics may be used as a starting point for a quantum theory of random lasers.