Seán Gomes
Abstract
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We show that under generic conditions, the quantisation of a $1$-parameter family of KAM perturbations $P(x,ξ;t)$ 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 $t\in (0,δ)$.
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We show that under generic conditions, the quantisation of a $1$-parameter family of KAM perturbations $P(x,ξ;t)$ 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 $t\in (0,δ)$.
Key concepts: Ergodic theory, Degenerate energy levels, Kolmogorov–Arnold–Moser theorem, Integrable system, Hamiltonian (control theory), Quantum, Mathematical physics, Measure (data warehouse)