Observation of Phase Space Dynamics of Inverted Harmonic Oscillator

Abstract:We have experimentally realized a parabolic potential barrier for surface gravity water waves. The analogy between the resulting wave equation and the Schrodinger equation for the inverted harmonic oscillator (IHO) enables us to study the propagation of quantum-mechanical wave packets with different average energies in this iconic scattering model. We observe a clear boundary in the phase-space dynamics, namely the separatrix, which distinguishes wave packets with energies below the maximum of the IHO potential from those with energies above it. In the former case, the wave packet is blocked, whereas in the latter case, it is transmitted. We also measure the corresponding variation in momentum during this process.

Classical Physics (physics.class-ph); Fluid Dynamics (physics.flu-dyn); Quantum Physics (quant-ph)

arXiv:2607.18297 [physics.class-ph]

(or arXiv:2607.18297v1 [physics.class-ph] for this version)

https://doi.org/10.48550/arXiv.2607.18297 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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