Preprint Article Version 1 This version is not peer-reviewed

Bouncing oil droplets, de Broglie's quantum thermostat and convergence to equilibrium

Version 1 : Received: 28 August 2018 / Approved: 28 August 2018 / Online: 28 August 2018 (11:34:09 CEST)

A peer-reviewed article of this Preprint also exists.

Hatifi, M.; Willox, R.; Colin, S.; Durt, T. Bouncing Oil Droplets, de Broglie’s Quantum Thermostat, and Convergence to Equilibrium. Entropy 2018, 20, 780. Hatifi, M.; Willox, R.; Colin, S.; Durt, T. Bouncing Oil Droplets, de Broglie’s Quantum Thermostat, and Convergence to Equilibrium. Entropy 2018, 20, 780.

Journal reference: Entropy 2018, 20, 780
DOI: 10.3390/e20100780

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 behaviour. 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.

Subject Areas

Bouncing oil droplets; Stochastic quantum dynamics; de Broglie–Bohm theory; Quantum non-equilibrium; H-theorem; Ergodicity

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