Brownian motion in the pilot wave interpretation of de Broglie and relaxation to quantum equilibrium

Abstract

The pilot wave interpretation proposed by de Broglie and later by Bohm contains not only a dynamical ontology but also relies on a statistical assumption known as quantum equilibrium. In this work which follows our recent article [1] we develop a Langevin force description of the relaxation process which leads to quantum equilibrium. Based on a application of the Caldera-Leggett model for a thermal bath we show how a Brownian motion leads naturally to quantum relaxation.