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A major challenge to the control of infinite dimensional quantum systems is
the irreversibility which is often present in the system dynamics. Here we
consider systems with discrete-spectrum Hamiltonians operating over a Schwartz
space domain, and show that by utilizing the implications of the Quantum
Recurrence Theorem this irreversibility may be overcome, in the case of
individual states more generally, but also in certain specified cases over
larger subsets of the Hilbert space. We discuss briefly the possibility of
using these results in the control of infinite dimensional coupled harmonic
oscillators, and also draw attention to some of the issues and open questions
arising from this and related work.

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