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Long-lived states and irregular dynamics in inelastic collisions: analysis of a polygon billiard model

The formation of long-lived collision complexes and the irregular, chaotic dynamics of such systems is studied for a simplified billiard-type model. The model describes the collinear collisions of an 'atom' with a 'molecule', which can be temporarily vibrationally excited. Assuming square-well interactions the system reduces to a polygon billiard, whose classical dynamics is determined by discrete mapping equations. Closed form results can be obtained by using the theory of interval exchange transformations. The nature of irregular dynamics for this scattering system is clarified and the complicated structure of the collisional lifetime function-dependent on the initial conditions-is analysed in detail.