What is it about?

If you vertically vibrate an open container filled with oil, then under the right conditions, a droplet of the same oil will “walk” horizontally across the liquid surface while bouncing vertically. Each bounce of the droplet creates a decaying wave around itself, which in turn guides the horizontal motion of the droplet, resulting in a self-propelled wave–particle entity. Such a moving wave-particle entity can exhibit chaotic movements in certain regimes. We have shown theoretically that the equations that govern the motion of this wave-particle entity can be transformed to the equations that are very similar to the well known equations of chaos theory discovered by Lorenz.

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Why is it important?

Intriguingly, these millimeter sized macroscopic wave-particle entities have been shown to mimic several peculiar features that were previously thought to be exclusive to the microscopic quantum world. The complex chaotic motion of the wave-particle entity gives rise to coherent wave-like statistics that is typically observed with quantum particles. Hence, the connection to the well studied Lorenz chaos established in this work will provide a strong foundation in understanding how these coherent wave-like statistics emerge from the underlying chaotic movements of the wave-particle entity.

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This page is a summary of: Lorenz-like systems emerging from an integro-differential trajectory equation of a one-dimensional wave–particle entity, Chaos An Interdisciplinary Journal of Nonlinear Science, February 2022, American Institute of Physics,
DOI: 10.1063/5.0076162.
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