Pais-Uhlenbeck Oscillator with a Benign Friction Force

Abstract

It is shown that the Pais-Uhlenbeck oscillator with damping, considered by Nesterenko, is a special case of a more general oscillator that has not only a first order, but also a third order friction term. If the corresponding damping constants, α and β, are both positive and below certain critical values, then the system is stable. In particular, if α= - β, then we have the unstable Nesterenko's oscillator

6 pages, 1 figure; reference added; typos corrected

References in corpus (5)

• Stable Self-Interacting Pais-Uhlenbeck Oscillator
• Comments on the Dynamics of the Pais-Uhlenbeck Oscillator
• Supersymmetry vs ghosts
• On the instability of classical dynamics in theories with higher derivatives
• Some Comments on Ghosts and Unitarity: The Pais-Uhlenbeck Oscillator Revisited

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• A perturbation theory approach to the stability of the Pais-Uhlenbeck oscillator
• Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants
• Foundations of ghost stability
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• On Negative Energies, Strings, Branes, and Braneworlds: A Review of Novel Approaches
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• Higher order gravities and the Strong Equivalence Principle
• Entanglement of higher-derivative oscillators in holographic systems
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• Various disguises of the Pais-Uhlenbeck oscillator
• Nonlocal dynamics and infinite non-relativistic conformal symmetries
• Time dependent Pais-Uhlenbeck oscillator and its decomposition
• Lie symmetries and ghost-free representations of the Pais-Uhlenbeck model
• Conformal symmetry in damped Pais-Uhlenbeck oscillator
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• Conformal Gravity Redux: Ghost-turned-Tachyon
• A Non-Trivial Zero Length Limit of the Nambu-Goto String