Decay of the polarization field in a Maxwell Bloch system

Frank Jochmann

doi:10.3934/dcds.2003.9.663

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2003, Volume 9, Issue 3: 663-676. Doi: 10.3934/dcds.2003.9.663

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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

Received: January 2002

Revised: November 2002

Published: May 2003

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Abstract

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 $t\rightarrow\infty$.

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Mathematics Subject Classification: 35Q60, 35L40, 78A35.

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