KAM Hamiltonians are not Quantum Ergodic

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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Veröffentlicht in:arXiv.org 2018-11
1. Verfasser: Gomes, Sean
Format: Artikel
Sprache:eng
Schlagworte:
Ergodic processes
Mathematics - Analysis of PDEs
Parameters
Perturbation
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Beschreibung
Zusammenfassung: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 \(t\in (0,\delta)\).
ISSN:2331-8422
DOI:10.48550/arxiv.1811.07718