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Effect of isolation on two-particle correlations in pilot-wave hydrodynamics
Phys. Rev. Fluids 7, 093604 – Published 16 September, 2022
DOI: https://doi.org/10.1103/PhysRevFluids.7.093604
Abstract
We present a numerical investigation on the effect of isolation imposed on two previously correlated walking droplets. These two bouncing droplets oscillate horizontally, confined to separate cavities placed at a distance. Nachbin [Chaos 28, 096110 (2018)] showed that the droplets are coupled through the underlying wave field of the multicavity system, resulting in nonseparable subsystems: their respective probability distributions cannot be inferred through an individual solitary droplet. Beyond correlated, the droplets are statistically indistinguishable, highlighting their intrinsically related statistics. Isolation is imposed through a wide barrier which abruptly halts the long-range wave-mediated interactions between droplets. Shortly after, both droplets transition to new cycles in phase space. The postisolation phase-space histograms reflect new and effectively identical probability density distributions. The particles' new energy level is higher than if the droplets had been isolated at all times. The new energy level observed, and sustained beyond isolation, is shown to be related with long-range disturbances existing prior to isolation. The postisolation change of phase-space cycles is faster than any possible propagation of information between subsystems. The statistical droplet pairing is therefore associated to preexisting correlations between particles. The intrinsic statistical relation of the bipartite system adjusts itself to new configurations where statistical indistinguishability persists even after the particles are set into isolation.
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