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

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.