{"id":4833,"date":"2018-04-01T01:56:00","date_gmt":"2018-04-01T01:56:00","guid":{"rendered":"http:\/\/thales.mit.edu\/bush\/?p=4833"},"modified":"2021-04-15T02:11:25","modified_gmt":"2021-04-15T02:11:25","slug":"dynamics-emergent-statistics-and-the-mean-pilot-wave-potential-of-walking-droplets","status":"publish","type":"post","link":"https:\/\/thales.mit.edu\/bush\/index.php\/2018\/04\/01\/dynamics-emergent-statistics-and-the-mean-pilot-wave-potential-of-walking-droplets\/","title":{"rendered":"The mean-pilot-wave potential"},"content":{"rendered":"\n
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A particle moves along a line, localized by its own wave field. In the high-memory limit, it navigates its mean-pilot-wave potential, which plays the role of the quantum potential in Bohmian mechanics.<\/figcaption><\/figure>\n\n\n\n

A millimetric droplet may bounce and self-propel on the surface of a vertically vibrating bath, where its horizontal \u201cwalking\u201d motion is induced by repeated impacts with its accompanying Faraday wave field. For ergodic long-time dynamics, we derive the relationship between the droplet\u2019s 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\u2019s 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.<\/p>\n\n\n\n

See paper: Durey, M., Milewski, P.A. and Bush, J.W.M., Chaos<\/em> (2018).<\/a><\/p>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":5,"featured_media":4835,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15,3],"tags":[],"class_list":["post-4833","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-hydrodynamic-quantum-analogues","category-pilot-wave-hydrodynamics","entry"],"yoast_head":"\nThe mean-pilot-wave potential - John W. M. 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