[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