Self-organization into quantized eigenstates of a classical wave-driven particle

Stéphane Perrard, Matthieu Labousse, Marc Miskin, Emmanuel Fort () and Yves Couder
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Stéphane Perrard: Matières et Systèmes Complexes, Université Paris Diderot, CNRS UMR 7057
Matthieu Labousse: Institut Langevin, ESPCI ParisTech, CNRS UMR 7587
Marc Miskin: Matières et Systèmes Complexes, Université Paris Diderot, CNRS UMR 7057
Emmanuel Fort: Institut Langevin, ESPCI ParisTech, CNRS UMR 7587
Yves Couder: Matières et Systèmes Complexes, Université Paris Diderot, CNRS UMR 7057

Nature Communications, 2014, vol. 5, issue 1, 1-8

Abstract: Abstract A growing number of dynamical situations involve the coupling of particles or singularities with physical waves. In principle these situations are very far from the wave particle duality at quantum scale where the wave is probabilistic by nature. Yet some dual characteristics were observed in a system where a macroscopic droplet is guided by a pilot wave it generates. Here we investigate the behaviour of these entities when confined in a two-dimensional harmonic potential well. A discrete set of stable orbits is observed, in the shape of successive generalized Cassinian-like curves (circles, ovals, lemniscates, trefoils and so on). Along these specific trajectories, the droplet motion is characterized by a double quantization of the orbit spatial extent and of the angular momentum. We show that these trajectories are intertwined with the dynamical build-up of central wave-field modes. These dual self-organized modes form a basis of eigenstates on which more complex motions are naturally decomposed.

Date: 2014
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DOI: 10.1038/ncomms4219

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