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Quantumlike statistics of deterministic wave-particle interactions in a circular cavity

Tristan Gilet*

  • Microfluidics Lab, Department of Aerospace and Mechanics, University of Liège, B-4000 Liège, Belgium

  • *Tristan.Gilet@ulg.ac.be
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Phys. Rev. E 93, 042202 – Published 5 April, 2016

DOI: https://doi.org/10.1103/PhysRevE.93.042202

Abstract

A deterministic low-dimensional iterated map is proposed here to describe the interaction between a bouncing droplet and Faraday waves confined to a circular cavity. Its solutions are investigated theoretically and numerically. The horizontal trajectory of the droplet can be chaotic: it then corresponds to a random walk of average step size equal to half the Faraday wavelength. An analogy is made between the diffusion coefficient of this random walk and the action per unit mass ℏ/m of a quantum particle. The statistics of droplet position and speed are shaped by the cavity eigenmodes, in remarkable agreement with the solution of Schrödinger equation for a quantum particle in a similar potential well.

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Phys. Rev. E 93, 042202– Published 5 April, 2016
  • Received 21 January 2016

©2016 American Physical Society

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