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Tunneling of walking oil drops.

M. Levinsen

Published 2025 in Physical Review E

ABSTRACT

Walkers are oil drops surfing on a vibrated oil surface and driven by their self-generated capillary waves. Since some of the first measurements on walkers seemingly showed quantum-like behavior, walkers have been considered a model system for a hydrodynamic pilot-wave system. An early experiment showed that the passage of the walker over a submerged barrier resulted in what was coined "unpredictable walker tunneling" in analogy with quantum tunneling. Together with the double slit experiment, tunneling is one of the fundamental phenomena that show the probabilistic nature of quantum mechanics. A later experiment that refined the measurement of position and timing of the walker narrowed the region where transmission changed from 0 to 1 by a factor 10 but still found "unpredictable tunneling." However, at a certain small distance close to the rim of the barrier, predictability sets in, and separation between reflected and transmitted trajectories is observed. After careful analysis of identified noise sources, the authors find that neither noise nor insufficient knowledge of initial conditions alone could explain the unpredictability. They therefore conclude that it is more likely due to changes in the drop's vertical dynamics arising when it interacts with the barrier. They also analyzed a quantum particle impinging on a barrier by step-wise collapsing the wave function and showed a similar behavior for this. Here we revisit the "tunneling" of walkers. Enforcing a stringent control of temperature in all aspects of the experiment results in the observation of a much sharper transition, much like that of a classical system, reducing the unpredictability by another factor of 10. Apart from varying the velocity of the walker by changing the drop size, we varied it by changing the amplitude of the drive. We furthermore found that a micron-size change in fluid height changes transmission from 0 to 1. The observed sharpness of the transition suggests that in a noise-free environment the transition would be truly abrupt, at least in the regions of phase-space for the drop that have been investigated so far.

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