Numerical studies of the approach to quantum equilibrium in de Broglie-Bohm theory

University of Cambridge, U.K.

We illustrate through explicit numerical simulations how non-relativistic quantum mechanics emerges as the 'quantum equililbrium' of the particle dyanamics of de Broglie-Bohm pilot-wave theory. The usual Born-rule probability densities emerge naturally, in the sense that sets of particles initially *not* distributed as the absolute square of the wave function are overwhelmingly likely to become so distributed over the course of time, subject to the usual statistical mechanical assumptions about initial conditions. The orthodox formalism of quantum mechanics (operators as observables, Born rule etc) thus emerges only as an equilibrium phenomenology and is not required at the fundamental level, where all we have is a partial differential equation for a field in configuration space plus a guidance equation. Illustrative simulations are presented for particles in two- and three-dimensional infinite potential square wells, and through these we seek an improvement in our understanding of timescales for relaxation to quantum equilibrium. This is likely to be of use in the development of models of relaxation in the early universe, with a view to constraining possible violations of the Born rule in inflationary cosmology.