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The pilot-wave dynamics of walking droplets

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Published on Dec 19, 2012

By Daniel M. Harris & John W. M. Bush
Department of Mathematics, MIT

Further information:
http://math.mit.edu/~bush/?page_id=484

Background:
It has been known for some time that a drop can bounce indefinitely on the surface of a vibrating fluid bath [1]. Recently it has come to light that millimetric droplets can propel themselves across the surface of a vibrating fluid bath by virtue of their pilot-wave dynamics, and that these walking droplets exhibit several features previously thought to be exclusive to the microscopic quantum realm, including single-particle diffraction, tunneling, quantized orbits and orbital level splitting [2, 3, 4, 5, 6, 7, 8].

In the video, we explore the pilot-wave dynamics of walking droplets. We first review the basic principles of the walking droplet system and then present the results of an experimental investigation of a walking droplet confined to circular domain. We demonstrate that a coherent statistical behavior emerges from the complex underlying dynamics, and that the statistics is prescribed by a wave function satisfying a linear wave equation. Our study indicates that this hydrodynamic system is closely related to the physical picture of quantum dynamics envisaged by de Broglie, in which rapid oscillations originating in the particle give rise to a guiding wave field [9, 10]. According to de Broglie's double-wave solution [10], the particle is guided by a real wave in such a way as to execute a dynamics whose statistics are described by standard quantum theory. The statistical behaviour of the walking droplets is similar to that of electrons in quantum corrals experiments [11]. This video is a winner of the Gallery of Fluid Motion 2012, an annual showcase of fluid dynamics videos. A more complete study of walkers in confined geometries has recently been published. [12].

[1] J. Walker. Drops of liquid can be made to float on the liquid. What enables them to do so? Scientific American, 238-6:151-158, 1978.

[2] Y. Couder, E. Fort, C.H. Gautier, and A. Boudaoud. From bouncing to floating: non-coalescence of drops on a fluid bath. Phys. Rev. Lett., 94:177801, 2005.

[3] S. Protiere, A. Boudaoud, and Y. Couder. Particle wave association on a fluid interface. J. Fluid Mech., 554:85-108, 2006.

[4] Y. Couder and E. Fort. Single particle diraction and interference at a macroscopic scale. Phys. Rev. Lett., 97:154101, 2006.

[5] A. Eddi, E. Fort, F. Moisy, and Y. Couder. Unpredictable tunneling of a classical wave-particle association. Phys. Rev. Lett., 102:240401, 2009.

[6] E. Fort, A. Eddi, A. Boudaoud, J. Moukhtar, and Y. Couder. Path-memory induced quantization of classical orbits. Proc. Nat. Acad. Sci., 107(41):17515{17520, 2010.

[7] J. W. M. Bush. Quantum mechanics writ large. Proc. Nat. Acad. Sci., 107:17455-17456, 2010.

[8] A. Eddi, J. Moukhtar, S. Perrard, E. Fort, and Y. Couder. Level splitting at macroscopic scale. Phys. Rev. Lett., 108:264503, 2012.

[9] L. de Broglie. Ondes et mouvements. Gautier Villars, Paris, 1926.

[10] L. de Broglie. Interpretation of quantum mechanics by the double solution theory. Annales de la Fondation Louis de Broglie, 12:1-23, 1987.

[11] M. F. Crommie, C. P. Lutz, and D. M. Eigler. Connement of electrons to quantum corrals on a metal surface. Science, 262:218-220, 1993.

[12] D. M. Harris, J. Moukhtar, E. Fort, Y. Couder, and J.W.M. Bush. Wave-like statistics from pilot-wave dynamics in a circular corral. Phys. Rev. E, 88, 011001(R), 2013.

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