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Entropy 2018, 20(10), 780; https://doi.org/10.3390/e20100780

Bouncing Oil Droplets, de Broglie’s Quantum Thermostat, and Convergence to Equilibrium

1
Aix Marseille Université, CNRS, Centrale Marseille, Institut Fresnel UMR 7249, 13013 Marseille, France
2
Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
3
Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil
*
Author to whom correspondence should be addressed.
Received: 24 August 2018 / Revised: 1 October 2018 / Accepted: 3 October 2018 / Published: 11 October 2018
(This article belongs to the Special Issue Emergent Quantum Mechanics – David Bohm Centennial Perspectives)
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Abstract

Recently, the properties of bouncing oil droplets, also known as “walkers,” have attracted much attention because they are thought to offer a gateway to a better understanding of quantum behavior. They indeed constitute a macroscopic realization of wave-particle duality, in the sense that their trajectories are guided by a self-generated surrounding wave. The aim of this paper is to try to describe walker phenomenology in terms of de Broglie–Bohm dynamics and of a stochastic version thereof. In particular, we first study how a stochastic modification of the de Broglie pilot-wave theory, à la Nelson, affects the process of relaxation to quantum equilibrium, and we prove an H-theorem for the relaxation to quantum equilibrium under Nelson-type dynamics. We then compare the onset of equilibrium in the stochastic and the de Broglie–Bohm approaches and we propose some simple experiments by which one can test the applicability of our theory to the context of bouncing oil droplets. Finally, we compare our theory to actual observations of walker behavior in a 2D harmonic potential well. View Full-Text
Keywords: bouncing oil droplets; stochastic quantum dynamics; de Broglie–Bohm theory; quantum non-equilibrium; H-theorem; ergodicity bouncing oil droplets; stochastic quantum dynamics; de Broglie–Bohm theory; quantum non-equilibrium; H-theorem; ergodicity
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Hatifi, M.; Willox, R.; Colin, S.; Durt, T. Bouncing Oil Droplets, de Broglie’s Quantum Thermostat, and Convergence to Equilibrium. Entropy 2018, 20, 780.

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