A model with chaotic scattering and reduction of wave packets

Some variants of Smilansky’s model of a particle interacting with harmonic oscillators are examined
in the framework of scattering theory. A dynamical proof is given of the existence of wave
operators. Analysis of a classical version of the model provides a transparent picture for the
spectral transition to which the quantum model owes its renown, and for the underlying dynamical
behaviour. The model is thereby classified as an extreme case of chaotic scattering, with aspects
related to wave packet reduction and irreversibility.

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