Tunneling with a hydrodynamic pilot-wave model

André Nachbin, Paul Milewski, John W M Bush

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Eddi et al. [Phys. Rev Lett. 102, 240401 (2009)] presented experimental results demonstrating the unpredictable tunneling of a classical wave-particle association as may arise when a droplet walking across the surface of a vibrating fluid bath approaches a submerged barrier. We here present a theoretical model that captures the influence of bottom topography on this wave-particle association and so enables us to investigate its interaction with barriers. The coupled wave-droplet dynamics results in unpredictable tunneling events. As reported in the experiments by Eddi et al. and as is the case in quantum tunneling [Gamow, Nature (London) 122, 805 (1928)], the predicted tunneling probability decreases exponentially with increasing barrier width. In the parameter regimes examined, tunneling between two cavities suggests an underlying stationary ergodic process for the droplet's position.
Original languageEnglish
Article number034801
JournalPhysical Review Fluids
Issue number3
Publication statusPublished - 30 Mar 2017


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