Reference : Quantumlike statistics of deterministic wave-particle interactions in a circular cavity
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Physics
http://hdl.handle.net/2268/201674
Quantumlike statistics of deterministic wave-particle interactions in a circular cavity
English
Gilet, Tristan mailto [Université de Liège > Département d'aérospatiale et mécanique > Microfluidique >]
2016
Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics
American Physical Society
93
042202
Yes (verified by ORBi)
International
1539-3755
1550-2376
College Park
MD
[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.
http://hdl.handle.net/2268/201674
10.1103/PhysRevE.93.042202

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