dorsal/arxiv
View SchemaAre Bohmian trajectories real? On the dynamical mismatch between de Broglie-Bohm and classical dynamics in semiclassical systems
| Authors | A. Matzkin, V. Nurock |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0609172 |
| URL | https://arxiv.org/abs/quant-ph/0609172 |
| DOI | 10.1016/j.shpsb.2007.04.005 |
| Journal | Studies in Hist. and Philosophy of Science B, 39, 17, 2008. [Published version is slightly different and carries the title "Classical and Bohmian trajectories in semiclassical systems: Mismatch in dynamics, mismatch in reality?" ] |
Abstract
The de Broglie-Bohm interpretation of quantum mechanics aims to give a realist description of quantum phenomena in terms of the motion of point-like particles following well-defined trajectories. This work is concerned by the de Broglie-Bohm account of the properties of semiclassical systems. Semiclassical systems are quantum systems that display the manifestation of classical trajectories: the wavefunction and the observable properties of such systems depend on the trajectories of the classical counterpart of the quantum system. For example the quantum properties have a regular or disordered aspect depending on whether the underlying classical system has regular or chaotic dynamics. In contrast, Bohmian trajectories in semiclassical systems have little in common with the trajectories of the classical counterpart, creating a dynamical mismatch relative to the quantum-classical correspondence visible in these systems. Our aim is to describe this mismatch (explicit illustrations are given), explain its origin, and examine some of the consequences on the status of Bohmian trajectories in semiclassical systems. We argue in particular that semiclassical systems put stronger constraints on the empirical acceptability and plausibility of Bohmian trajectories because the usual arguments given to dismiss the mismatch between the classical and the de Broglie-Bohm motions are weakened by the occurrence of classical trajectories in the quantum wavefunction of such systems.
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"abstract": "The de Broglie-Bohm interpretation of quantum mechanics aims to give a\nrealist description of quantum phenomena in terms of the motion of point-like\nparticles following well-defined trajectories. This work is concerned by the de\nBroglie-Bohm account of the properties of semiclassical systems. Semiclassical\nsystems are quantum systems that display the manifestation of classical\ntrajectories: the wavefunction and the observable properties of such systems\ndepend on the trajectories of the classical counterpart of the quantum system.\nFor example the quantum properties have a regular or disordered aspect\ndepending on whether the underlying classical system has regular or chaotic\ndynamics. In contrast, Bohmian trajectories in semiclassical systems have\nlittle in common with the trajectories of the classical counterpart, creating a\ndynamical mismatch relative to the quantum-classical correspondence visible in\nthese systems. Our aim is to describe this mismatch (explicit illustrations are\ngiven), explain its origin, and examine some of the consequences on the status\nof Bohmian trajectories in semiclassical systems. We argue in particular that\nsemiclassical systems put stronger constraints on the empirical acceptability\nand plausibility of Bohmian trajectories because the usual arguments given to\ndismiss the mismatch between the classical and the de Broglie-Bohm motions are\nweakened by the occurrence of classical trajectories in the quantum\nwavefunction of such systems.",
"arxiv_id": "quant-ph/0609172",
"authors": [
"A. Matzkin",
"V. Nurock"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1016/j.shpsb.2007.04.005",
"journal_ref": "Studies in Hist. and Philosophy of Science B, 39, 17, 2008.\n [Published version is slightly different and carries the title \"Classical and\n Bohmian trajectories in semiclassical systems: Mismatch in dynamics, mismatch\n in reality?\" ]",
"title": "Are Bohmian trajectories real? On the dynamical mismatch between de Broglie-Bohm and classical dynamics in semiclassical systems",
"url": "https://arxiv.org/abs/quant-ph/0609172"
},
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