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Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants / Nicolas Boulanger in The European Physical Journal C [périodique électronique], 79 (2019)  

Public ISBD [article]  inThe European Physical Journal C [périodique électronique] > 79 (2019) Titre : Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants Type de document : document électronique Auteurs : Nicolas Boulanger ; Fabien Buisseret ; Frédéric Dierick ; Olivier White Année de publication : 2019 Langues : Anglais (eng) Résumé : The status of classical stability in higher-derivative systems is still subject to discussions. In this note, we argue that, contrary to general belief, many higher-derivative systems are classically stable. The main tool to see this property are Nekhoroshev’s estimates relying on the action-angle formulation of classical mechanics. The latter formulation can be reached provided the Hamiltonian is separable, which is the case for higher-derivative harmonic oscillators. The Pais–Uhlenbeck oscillators appear to be the only type of higher-derivative harmonic oscillator with stable classical dynamics. A wide class of interaction potentials can even be added that preserve classical stability. Adiabatic invariants are built in the case of a Pais–Uhlenbeck oscillator slowly changing in time; it is shown indeed that the dynamical stability is not jeopardised by the time-dependent perturbation. En ligne : https://link.springer.com/article/10.1140/epjc/s10052-019-6569-y Permalink : ./index.php?lvl=notice_display&id=84495 [article] Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants [document électronique] / Nicolas Boulanger ; Fabien Buisseret ; Frédéric Dierick ; Olivier White . - 2019. Langues : Anglais (eng) in The European Physical Journal C [périodique électronique] > 79 (2019) Résumé : The status of classical stability in higher-derivative systems is still subject to discussions. In this note, we argue that, contrary to general belief, many higher-derivative systems are classically stable. The main tool to see this property are Nekhoroshev’s estimates relying on the action-angle formulation of classical mechanics. The latter formulation can be reached provided the Hamiltonian is separable, which is the case for higher-derivative harmonic oscillators. The Pais–Uhlenbeck oscillators appear to be the only type of higher-derivative harmonic oscillator with stable classical dynamics. A wide class of interaction potentials can even be added that preserve classical stability. Adiabatic invariants are built in the case of a Pais–Uhlenbeck oscillator slowly changing in time; it is shown indeed that the dynamical stability is not jeopardised by the time-dependent perturbation. En ligne : https://link.springer.com/article/10.1140/epjc/s10052-019-6569-y Permalink : ./index.php?lvl=notice_display&id=84495

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