HIGH FREQUENCY BEHAVIOR OF THE MAXWELL–BLOCH MODEL WITH RELAXATION: CONVERGENCE TO THE SCHRÖDINGER-RATE SYSTEM

DOI10.1142/S0219891612500129zbMath1264.81353arXiv1007.4342OpenAlexW2964029017MaRDI QIDQ4649844

Publication date: 15 November 2012

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.4342

zbMATH Keywords

density matrix weak interaction rate equations paraxial approximation high-frequency limit

Mathematics Subject Classification ID

Diffraction, scattering (78A45) Quantum optics (81V80) PDEs in connection with quantum mechanics (35Q40) Maxwell equations (35Q61)

Cites Work

Unnamed Item
Unnamed Item
Asymptotic solutions of oscillatory initial value problems
Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves
Transparent nonlinear geometric optics and Maxwell-Bloch equations.
From the von Neumann equation to the quantum Boltzmann equation. II: Identifying the Born series
Secular growth estimates for hyperbolic systems.
Some considerations on the derivation of the nonlinear quantum Boltzmann equation
Hierarchy of models in quantum optics. From Maxwell-Bloch to nonlinear Schrödinger.
STUDY OF A MATHEMATICAL MODEL FOR STIMULATED RAMAN SCATTERING
Asymptotic problems for wave–particle interactions: quantum and classical models
Transverse Diffraction of Nonlinear Waves and Singular Rays
On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation
Non-derivation of the quantum Boltzmann equation from the periodic Von Neumann Equation
Periodic multiphase nonlinear diffractive optics with curved phases
Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation
FROM BLOCH MODEL TO THE RATE EQUATIONS II: THE CASE OF ALMOST DEGENERATE ENERGY LEVELS
Coherent and focusing multidimensional nonlinear geometric optics
A semi-classical picture of quantum scattering
Derivation of the transport equation for electrons moving through random impurities
Introducing physical relaxation terms in Bloch equations
From the von Neumann equation to the quantum Boltzmann equation in a deterministic framework.

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