Quantum Equilibrium in Stochastic de Broglie-Bohm-Bell Quantum Mechanics

TL;DR

This paper demonstrates through numerical simulations and theoretical analysis that the stochastic de Broglie-Bohm-Bell quantum mechanics naturally relaxes to quantum equilibrium without requiring special initial conditions or additional modifications.

Contribution

It provides evidence that the stochastic Bell formulation inherently leads to quantum equilibrium, eliminating the need for ad-hoc assumptions or coarse-graining.

Findings

Relaxation to quantum equilibrium occurs for arbitrary initial distributions.

Stochastic Bell dynamics naturally ensures relaxation without coarse-graining.

The results support the sufficiency of stochastic Bell mechanics for quantum equilibrium emergence.

Abstract

This paper investigates dynamical relaxation to quantum equilibrium in the stochastic de Broglie-Bohm-Bell formulation of quantum mechanics. The time-dependent probability distributions are computed as in a Markov process with slowly varying transition matrices. Numerical simulations, supported by exact results for the large-time behavior of sequences of (slowly varying) transition matrices, confirm previous findings that indicate that de Broglie-Bohm-Bell dynamics allows an arbitrary initial probability distribution to relax to quantum equilibrium; i.e., there is no need to make the ad-hoc assumption that the initial distribution of particle locations has to be identical to the initial probability distribution prescribed by the system's initial wave function. The results presented in this paper moreover suggest that the intrinsically stochastic nature of Bell's formulation, which is arguable most naturally formulated on an underlying discrete space-time, is sufficient to ensure dynamical relaxation to quantum equilibrium for a large class of quantum systems without the need to introduce coarse-graining or any other modification in the formulation.