Dynamics of forced coupled oscillators: classical phenomenology of infrared multiphoton absorption

Abstract

The classical mechanics of a system of two nonlinearly coupled oscillators of incommensurate frequencies driven by an oscillating electric field are studied. The presence of quasi-periodic and chaotic motion in the unforced system is shown to influence the nature of energy absorption. Two essentially different types of behavior are observed. In the first, energy is exchanged in a periodic manner between the system and the forcing field. The exact results are compared with perturbative analysis (based on Lie-transform techniques) employed in this regime. In the second regime, the energy exchange is erratic and a statistical analysis of a family of trajectories shows the role of the chaotic motion in the unforced system in the dissociation process. The results of the theory are compared with those obtained from an ensemble of exact classical trajectories and found to be in reasonable agreement.

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