Generalized Dicke states, or density matrix description of N 2-level atoms homogeneously coupled to the environment

Here we describe in brief how to treat a fully homogeneous system of N equal 2-level atoms coupled to the field of a bad cavity. Treatment is performed on full quantum level, without any approximations Consideration is based primarily on the preprint of S. Hartmann "Generalized Dicke states, arXiv:1201.1732, but is restricted to fully symmetric states only. "Full quantum symmetric.pdf" -- technical notes with description, "Natoms_FullQuantumSymmetric_functions.jl" and "test.jl" --- Julia scripts for simulation of a bad-cavity laser where the gain is formed by a system of such 2-level atoms subjected to incoherent pumping. Simulations are performed in 2 variants: with and without adiabatic elimination of the cavity field. File "