KAM Hamiltonians are not Quantum Ergodic
Abstract
We show that under generic conditions, the quantisation of a 1-parameter family of KAM perturbations P(x,;t) of a completely integrable and Kolmogorov non-degenerate Gevrey smooth Hamiltonian is not quantum ergodic, at least for a full measure subset of the parameter t∈ (0,δ).
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