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May  2003, 9(3): 663-676. doi: 10.3934/dcds.2003.9.663

Decay of the polarization field in a Maxwell Bloch system

Frank Jochmann 1,

1. 

Fakultät II - Institut für Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany

Received  January 2002 Revised  November 2002 Published  February 2003

The Maxwell-Bloch equations describing the propagation of electromagnetic waves in a gas of quantum mechanical systems with two energy levels is investigated. The system under consideration consists of a generally nonlinear second order system of differential equations for the dielectrical polarization and the density coupled with Maxwell's equations for the electromagnetic field. The goal is to show decay of the polarization field for $t\rightarrow\infty$.
Keywords: nonlinear polarization, asymptotic behaviour., initial-boundary-value problem, Maxwell’s equations.
Mathematics Subject Classification: 35Q60, 35L40, 78A3.
Citation: Frank Jochmann. Decay of the polarization field in a Maxwell Bloch system. Discrete and Continuous Dynamical Systems, 2003, 9 (3) : 663-676. doi: 10.3934/dcds.2003.9.663
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