KAM Hamiltonians are not Quantum Ergodic
We show that under generic conditions, the quantisation of a \(1\)-parameter family of KAM perturbations \(P(x,\xi;t)\) 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 \(t\in (0,\delta)\).
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| creator | Gomes, Sean |
| description | We show that under generic conditions, the quantisation of a \(1\)-parameter family of KAM perturbations \(P(x,\xi;t)\) 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 \(t\in (0,\delta)\). |
| doi_str_mv | 10.48550/arxiv.1811.07718 |
| format | Article |
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| subjects | Ergodic processes Mathematics - Analysis of PDEs Parameters Perturbation |
| title | KAM Hamiltonians are not Quantum Ergodic |
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