The conjunction of atom-cavity physics and photonic structures (``solid light systems) offers new opportunities in terms of more device functionality and the probing of designed emulators of condensed matter systems. By analogy to the canonical one-e
lectron approximation of solid state physics, we propose a one-polariton approximation to study these systems. Using this approximation we apply Bloch states to the uniformly tuned Jaynes-Cummings-Hubbard model to analytically determine the energy band structure. By analyzing the response of the band structure to local atom-cavity control we explore its application as a quantum simulator and show phase transition features absent in mean field theory. Using this novel approach for solid light systems we extend the analysis to include detuning impurities to show the solid light analogy of the semiconductor. This investigation also shows new features with no semiconductor analog.
There has been recent debate over the use of the Boltzmann property in the kinetic equations describing dense neutrino systems such as early Universe and Supernova core. A technique developed by Bell, Rawlinson, and Sawyer utilises the flavour evolut
ion timescales of the neutrino systems to test the validity of this assumption. The Friedland-McKellar-Okuniewicz (FMO) many-body neutrino model was developed to conduct this test. It was concluded by its authors, using the Bell-Rawlinson-Sawyer timescale test, that the model lent support to the Boltzmann property assumption. We developed kinetic equations for the FMO model. By direct analysis of the kinetic equations we find, in stark contrast to Friedland et al., that in fact the Boltzmann property assumption does breakdown in the FMO model. We have shown that the Bell-Rawlinson-Sawyer timescale technique can only be used to invalidate the Boltzmann property but not validate it.
