Finite flux solutions of the quantum Boltzmann equation and semiconductor lasers

We propose and illustrate in the context of the semiconductor laser that, i n nonequilibrium fermionic systems with sources and sinks, the family of fi nite flux stationary solutions of the quantum Boltzmann equation is central and more important then the zero flux Fermi-Dirac spectrum. We present the quantum analog of the finite flux Kolmogorov spectra which are central to understanding nonequilibrium classical systems such as high Reynolds number hydrodynamics and the wave turbulence encountered in water waves, plasmas, and optics. In particular. we show how semiconductor laser efficiency can be improved by maximizing the flux of carriers (electrons and holes) toward s the lasing frequencies.