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

TL;DR

This paper develops a phenomenological theory connecting bouncing oil droplets, quantum behavior, and de Broglie-Bohm dynamics, analyzing how modifications affect relaxation to quantum equilibrium and proposing experiments to test these ideas.

Contribution

It introduces a new phenomenological framework linking oil droplet experiments with quantum dynamics, including an H-theorem for Nelson dynamics and comparative analysis with de Broglie-Bohm theory.

Findings

Proves an H-theorem for relaxation to quantum equilibrium under Nelson dynamics.

Analyzes differences in equilibrium onset between Nelson and de Broglie-Bohm approaches.

Suggests experiments to test the applicability of the theory to bouncing oil droplets.

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 constitute indeed 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 develop a phenomenological theory for the behavior of walkers in terms of de Broglie-Bohm and Nelson dynamics. We study in particular how modifications of the de Broglie pilot-wave theory, \`a la Nelson, affect the process of relaxation to quantum equilibrium, and prove an H-theorem for the relaxation to quantum equilibrium under Nelson dynamics. We compare the onset of equilibrium in the Nelson and de Broglie-Bohm approaches and we also propose some simple experiments by which one can test the applicability of our theory to the context of bouncing oil droplets.