Relaxation to quantum equilibrium for Dirac fermions in the de Broglie–Bohm pilot-wave theory
Author(s)
Colin, Samuel
Griffith University Author(s)
Year published
2012
Metadata
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Numerical simulations indicate that the Born rule does not need to be postulated in the de Broglie-Bohm pilot-wave theory, but tends to arise dynamically (relaxation to quantum equilibrium). These simulations were done for a particle in a two-dimensional box whose wave function obeys the non-relativistic Schr椩nger equation and is therefore scalar. The chaotic nature of the de Broglie-Bohm trajectories, thanks to the nodes of the wave function which yield to vortices, is crucial for a fast relaxation to quantum equilibrium. For spinors, we typically do not expect any node. However, in the case of the Dirac equation, the de ...
View more >Numerical simulations indicate that the Born rule does not need to be postulated in the de Broglie-Bohm pilot-wave theory, but tends to arise dynamically (relaxation to quantum equilibrium). These simulations were done for a particle in a two-dimensional box whose wave function obeys the non-relativistic Schr椩nger equation and is therefore scalar. The chaotic nature of the de Broglie-Bohm trajectories, thanks to the nodes of the wave function which yield to vortices, is crucial for a fast relaxation to quantum equilibrium. For spinors, we typically do not expect any node. However, in the case of the Dirac equation, the de Broglie-Bohm velocity field has vorticity even in the absence of nodes. This observation raises the question of the origin of relaxation to quantum equilibrium for fermions. In this article, we provide numerical evidence to show that Dirac particles also undergo relaxation, by simulating the evolution of various non-equilibrium distributions for two-dimensional systems (the two-dimensional Dirac oscillator and the Dirac particle in a two-dimensional spherical step potential).
View less >
View more >Numerical simulations indicate that the Born rule does not need to be postulated in the de Broglie-Bohm pilot-wave theory, but tends to arise dynamically (relaxation to quantum equilibrium). These simulations were done for a particle in a two-dimensional box whose wave function obeys the non-relativistic Schr椩nger equation and is therefore scalar. The chaotic nature of the de Broglie-Bohm trajectories, thanks to the nodes of the wave function which yield to vortices, is crucial for a fast relaxation to quantum equilibrium. For spinors, we typically do not expect any node. However, in the case of the Dirac equation, the de Broglie-Bohm velocity field has vorticity even in the absence of nodes. This observation raises the question of the origin of relaxation to quantum equilibrium for fermions. In this article, we provide numerical evidence to show that Dirac particles also undergo relaxation, by simulating the evolution of various non-equilibrium distributions for two-dimensional systems (the two-dimensional Dirac oscillator and the Dirac particle in a two-dimensional spherical step potential).
View less >
Journal Title
Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences
Volume
468
Issue
2140
Subject
Quantum Physics not elsewhere classified
Mathematical Aspects of Classical Mechanics, Quantum Mechanics and Quantum Information Theory
Mathematical Sciences
Physical Sciences
Engineering