Reference : Quantumlike statistics of deterministic wave-particle interactions in a circular cavity
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Physics
Quantumlike statistics of deterministic wave-particle interactions in a circular cavity
Gilet, Tristan mailto [Université de Liège > Département d'aérospatiale et mécanique > Microfluidique >]
Physical Review. E ,Statistical, Nonlinear, and Soft Matter Physics
American Physical Society
Yes (verified by ORBi)
College Park
[en] Walking droplets ; Quantum mechanics
[en] 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 h/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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2016-PhysRevE.93(postprint author).pdfAuthor postprint6.61 MBView/Open

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