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- Title
Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants.
- Authors
Boulanger, Nicolas; Buisseret, Fabien; Dierick, Frédéric; White, Olivier
- Abstract
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.
- Subjects
HARMONIC oscillators; ADIABATIC invariants; INVARIANTS (Mathematics); HARMONIC motion; RESONATORS
- Publication
European Physical Journal C -- Particles & Fields, 2019, Vol 79, Issue 1, p1
- ISSN
1434-6044
- Publication type
Article
- DOI
10.1140/epjc/s10052-019-6569-y