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We present a number of fresh perspectives on pilot-wave hydrodynamics, the field initiated in 2005 by Couder and Fort's discovery that millimetric droplets self-propelling along the surface of a vibrating bath can capture certain features of quantum systems. A recurring theme will be that pilot-wave hydrodynamics furnishes a classical framework for reproducing many quantum phenomena and allows one to rationalize such phenomena mechanistically, from a local realist perspective, obviating the need to appeal to quantum nonlocality. The distinction is drawn between hydrodynamic pilot-wave theory and its quantum counterparts, Bohmian mechanics, the Bohm–Vigier stochastic pilot-wave theory, and de Broglie's theory of the double-solution. Each of these quantum predecessors provide a valuable touchstone as we take the physical picture engendered in the walking droplets and extend it into the quantum realm via theoretical modeling. Emphasis is given to recent developments in the field, both experimental and conceptual, and to forecasting potentially fruitful new directions. 

A millimetric droplet may bounce and self-propel on the surface of a vertically vibrating bath, where its horizontal “walking” motion is induced by repeated impacts with its accompanying Faraday wave field. For ergodic long-time dynamics, we derive the relationship between the droplet’s stationary statistical distribution and its mean wave field in a very general setting. We then focus on the case of a droplet subjected to a harmonic potential with its motion confined to a line. By analyzing the system’s periodic states, we reveal a number of dynamical regimes, including those characterized by stationary bouncing droplets trapped by the harmonic potential, periodic quantized oscillations, chaotic motion and wavelike statistics, and periodic wave-trapped droplet motion that may persist even in the absence of a central force. We demonstrate that as the vibrational forcing is increased progressively, the periodic oscillations become chaotic via the Ruelle-Takens-Newhouse route. We rationalize the role of the local pilot-wave structure on the resulting droplet motion, which is akin to a random walk. We characterize the emergence of wavelike statistics influenced by the effective potential that is induced by the mean Faraday wave field.