Dissipation induced Instabilities and the Mechanical Laser
Chaotic Dynamics
2007-05-23 v1
Abstract
We study the 1:1 resonance for perturbed Hamiltonian systems with small dissipative and energy injection terms. These perturbations of the 1:1 resonance exhibit dissipation induced instabilities. This mechanism allow us to show that a slightly pumping optical cavity is unstable when one takes into account the dissipative effects. The Maxwell-Bloch equations are the asymptotic normal form that describe this instability when energy is injected through forcing at zero frequency. We display a simple mechanical system, close to the 1:1 resonance, which is a mechanical analog of the Laser.
Cite
@article{arxiv.nlin/0103049,
title = {Dissipation induced Instabilities and the Mechanical Laser},
author = {Marcel G. Clerc and Jerrold E. Marsden},
journal= {arXiv preprint arXiv:nlin/0103049},
year = {2007}
}
Comments
4 pages, 2 figures