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Quantum-Classical Transition for Mixed States: The Scaled Von Neumann Equation
Version 1
: Received: 25 April 2023 / Approved: 25 April 2023 / Online: 25 April 2023 (10:19:58 CEST)
A peer-reviewed article of this Preprint also exists.
Mousavi, S.V.; Miret-Artés, S. Quantum Classical Transition for Mixed States: The Scaled Von Neumann Equation. Symmetry 2023, 15, 1184. Mousavi, S.V.; Miret-Artés, S. Quantum Classical Transition for Mixed States: The Scaled Von Neumann Equation. Symmetry 2023, 15, 1184.
Abstract
In this work, we propose a transition wave equation from quantum to classical regime in the framework of the von Neumann formalism for ensembles and then obtain an equivalent scaled equation. This leads us to develop a scaled statistical theory following the well-known Wigner-Moyal approach of quantum mechanics. This scaled nonequilibrium statistical mechanics has in it all the ingredients of the classical and quantum theory described in terms of a continuous parameter displaying all the dynamical regimes in-between the two extreme cases. Finally, a simple application of our scaled formalism consisting of reflection from a mirror by computing various quantities including probability density plots, scaled trajectories and arrival times are analyzed.
Keywords
Bohmian mechanics; Transition wave equation; Scaled Liouville-von Neumann equation; Scaled trajectories; Scaled Wigner-Moyal approach; Scaled Wigner distribution function
Subject
Physical Sciences, Theoretical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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