QUANTUM WEAK TURBULENCE WITH APPLICATIONS TO SEMICONDUCTOR-LASERS

Based on a model Hamiltonian appropriate for the description of fermio nic systems such as semiconductor lasers, we describe a natural asympt otic closure of the BBGKY hierarchy in complete analogy with that deri ved for classical weak turbulence. The main features of the interactio n Hamiltonian are the inclusion of full Fermi statistics containing Pa uli blocking and a simple, phenomenological, uniformly weak two-partic le interaction potential equivalent to the static screening approximat ion. We find a new class of solutions to the quantum kinetic equation which are analogous to the Kolmogorov spectra of hydrodynamics and cla ssical weak turbulence. They involve finite fluxes of particles and en ergy in momentum space and are particularly relevant for describing th e behavior of systems containing sources and sinks. We make a prima fa cie case that these finite flux solutions can be important in the cont ext of semiconductor lasers and show how they might be used to enhance laser performance. (C) 1998 Elsevier Science B.V. All rights reserved .