Quantum Weak Turbulence with Applications

to Semiconductor Lasers. Y.V. Lvov, R. Binder and A.C. Newell**Physica D, ****121**, pp. 317 - 343,(1998).

to Semiconductor Lasers. Y.V. Lvov, R. Binder and A.C. Newell

Department of Mathematics, The University of Arizona, Tucson, 85721 Arizona

Department of Physics, The University of Arizona, Tucson, 85721 Arizona

Optical Sciences Center, The University of Arizona, Tucson, 85721 Arizona

Department of Mathematics, University of Warwick, Coventry, CV47AL, UK

Based on a model Hamiltonian appropriate for
the description of fermionic systems such as semiconductor lasers, we
describe a natural asymptotic closure of the BBGKY hierarchy in
complete analogy with that derived for classical weak turbulence. The
main features of the interaction Hamiltonian are the inclusion of full
Fermi statistics containing Pauli blocking and a simple,
phenomenological, uniformly weak two particle interaction potential
equivalent to the static screening approximation. We find a new class
of solutions to the quantum kinetic equation which are analogous to
the Kolmogorov spectra of hydrodynamics and classical weak
turbulence. They involve finite fluxes of particles and energy in
momentum space and are particularly relevant for describing the
behavior of systems containing sources and sinks. We make a prima
facie case that these finite flux solutions can be important in the
context of semiconductor lasers and show how they might be used to
enhance laser performance.

- Introduction and General Discussion.

- Systematic Derivation of the
Kinetic Equation and Evolution equations for Higher Order Cumulants
- Basic Definitions and Evolution Equation
- Cumulants and their evolution.
- Asymptotic Expansions and Closure

- Analysis of the Kinetic Equation.

- Differential Kinetic Equation
- Derivation of Differential Quantum Kinetic Equation
- Solutions and properties of the DQKE
- Numerical Results.

- Application to Semiconductor Lasers
- Conclusions
- Acknowledgment
- Figure Captions
- Appendix. Diagrams
- Bibliography
- Figures
- About this document ...