In this talk I will be stating some results about spectral analysis of systems of PDEs. Specifically, a Weyl asymptotic is given for a class of systems containing not only certain quantum optics models such as the Jaynes-Cummings model, which is fundamental in Quantum Optics, but models of geometric differential complexes over R^n, too. Moreover, I discuss a quasi-clustering result for this class of positive systems. Finally, a meromorphic continuation of the spectral zeta function for semiregular Non-Commutative Harmonic Oscillators (NCHO) is given. By “semiregular system” we mean a pseudodifferential systems with a step j in the homogeneity of the jth term in the asymptotic expansion of the symbol. The aforementioned results were obtained jointly with Alberto Parmeggiani.