Abstract

We show that an infinite set of q-deformed relevant operators close a partial q-deformed Lie algebra under commutation with the Arik-Coon oscillator. The dynamics is described by the multicommutator [ H ̂ , …, [ H ̂ , O ̂ ] …] , that follows a power law which leads to a dynamical scaling. We study the dynamics of the Arik-Coon and anharmonic oscillators and analyze the role of q and the other parameters in the evolution of both systems.

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