Analysis of the mean values and fluctuations in the chaotic maser model

Recently obtained results on the quantum “grid” of mean values of observables in the energy representation for the maser model is here compared with the classical results calculated via the microcanonical mean values using the classical hamiltonian. Our main result is the evidence that such comparison does work for all regimes from regular to chaotic (but not necessarily ergodic). We show evidences that such quantum fluctuation around the classical average depend on the oscillations of the size and the position of the classical stable region merged in the chaotic sea. Also, depending on the choice of the observable being associated to compact phase space (spin) or infinite phase space (boson) the spreading around the mean can become larger or smaller.