Equation-of-motion method for full counting statistics: Steady-state superradiance

For the multimode Dicke model in a transport setting that exhibits collective boson transmissions, we construct the equation of motion for the cumulant-generating function. Approximating the exact system of equations at the level of the cumulant-generating function and system operators at lowest order allows us to recover master equation results of the full counting statistics for certain parameter regimes at very low computational cost. The thermodynamic limit, which is not accessible with the master equation approach, can be derived analytically for different approximations.