Quantum Equilibrium in Stochastic de Broglie-Bohm-Bell Quantum Mechanics
- URL: http://arxiv.org/abs/2207.01008v1
- Date: Sun, 3 Jul 2022 10:56:03 GMT
- Title: Quantum Equilibrium in Stochastic de Broglie-Bohm-Bell Quantum Mechanics
- Authors: Jeroen C. Vink
- Abstract summary: This paper investigates dynamical relaxation to quantum equilibrium in the de Broglie-Bohm-Bell formulation of quantum mechanics.
Numerical simulations confirm previous findings that indicate that de Broglie-Bohm-Bell dynamics allows an arbitrary initial probability distribution to relax to quantum equilibrium.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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