Conformal symmetry in damped Pais-Uhlenbeck oscillator

TL;DR

This paper explores conformal symmetry in a generalized damped Pais-Uhlenbeck oscillator, extending Bateman's models with higher derivatives that exhibit l-conformal Newton-Hooke symmetry, linking to the dynamics of damped oscillators.

Contribution

It introduces higher derivative generalizations of Bateman's damped oscillator models that possess l-conformal Newton-Hooke symmetry, connecting conformal symmetry with damped oscillator dynamics.

Findings

Constructed higher derivative models with conformal symmetry.

Linked generalized models to the damped Pais-Uhlenbeck oscillator.

Demonstrated symmetry properties in damped oscillator dynamics.

Abstract

Two Lagrangian formulations for describing of the damped harmonic oscillator have been introduced by Bateman. For these models we construct higher derivative generalization which enjoys the l-conformal Newton-Hooke symmetry. The dynamics of generalized systems corresponds to the damped Pais-Uhlenbeck oscillator for a particular choice of its frequencies.