### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 317-343 |

Number of pages | 27 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 121 |

Issue number | 3-4 |

State | Published - 1998 |

### Fingerprint

### Keywords

- BBGKY hierarchy
- Kolmogorov spectra
- Quantum kinetic equation
- Quantum weak turbulence
- Semiconductor laser

### ASJC Scopus subject areas

- Applied Mathematics
- Statistical and Nonlinear Physics

### Cite this

*Physica D: Nonlinear Phenomena*,

*121*(3-4), 317-343.

**Quantum weak turbulence with applications to semiconductor lasers.** / Lvov, Y. V.; Binder, Rudolf; Newell, Alan C.

Research output: Contribution to journal › Article

*Physica D: Nonlinear Phenomena*, vol. 121, no. 3-4, pp. 317-343.

}

TY - JOUR

T1 - Quantum weak turbulence with applications to semiconductor lasers

AU - Lvov, Y. V.

AU - Binder, Rudolf

AU - Newell, Alan C

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

KW - BBGKY hierarchy

KW - Kolmogorov spectra

KW - Quantum kinetic equation

KW - Quantum weak turbulence

KW - Semiconductor laser

UR - http://www.scopus.com/inward/record.url?scp=0032186801&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032186801&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032186801

VL - 121

SP - 317

EP - 343

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 3-4

ER -