  We study the emergence of collective dynamics in the integrable Hamiltonian
system of two finite ensembles of coupled harmonic oscillators. After
identification of a collective degree of freedom, the Hamiltonian is mapped
onto a model of Caldeira-Leggett type, where the collective coordinate is
coupled to an internal bath of phonons. In contrast to the usual
Caldeira-Leggett model, the bath in the present case is part of the system. We
derive an equation of motion for the collective coordinate which takes the form
of a damped harmonic oscillator. We show that the distribution of quantum
transition strengths induced by the collective mode is determined by its
classical dynamics.
