dorsal/arxiv
View SchemaOn the Role of Density Matrices in Bohmian Mechanics
| Authors | Detlef Duerr, Sheldon Goldstein, Roderich Tumulka, Nino Zanghi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0311127 |
| URL | https://arxiv.org/abs/quant-ph/0311127 |
| DOI | 10.1007/s10701-004-1983-9 |
| Journal | Foundations of Physics 35(3): 449-467 (2005) |
Abstract
It is well known that density matrices can be used in quantum mechanics to represent the information available to an observer about either a system with a random wave function (``statistical mixture'') or a system that is entangled with another system (``reduced density matrix''). We point out another role, previously unnoticed in the literature, that a density matrix can play: it can be the ``conditional density matrix,'' conditional on the configuration of the environment. A precise definition can be given in the context of Bohmian mechanics, whereas orthodox quantum mechanics is too vague to allow a sharp definition, except perhaps in special cases. In contrast to statistical and reduced density matrices, forming the conditional density matrix involves no averaging. In Bohmian mechanics with spin, the conditional density matrix replaces the notion of conditional wave function, as the object with the same dynamical significance as the wave function of a Bohmian system.
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"abstract": "It is well known that density matrices can be used in quantum mechanics to\nrepresent the information available to an observer about either a system with a\nrandom wave function (``statistical mixture\u0027\u0027) or a system that is entangled\nwith another system (``reduced density matrix\u0027\u0027). We point out another role,\npreviously unnoticed in the literature, that a density matrix can play: it can\nbe the ``conditional density matrix,\u0027\u0027 conditional on the configuration of the\nenvironment. A precise definition can be given in the context of Bohmian\nmechanics, whereas orthodox quantum mechanics is too vague to allow a sharp\ndefinition, except perhaps in special cases. In contrast to statistical and\nreduced density matrices, forming the conditional density matrix involves no\naveraging. In Bohmian mechanics with spin, the conditional density matrix\nreplaces the notion of conditional wave function, as the object with the same\ndynamical significance as the wave function of a Bohmian system.",
"arxiv_id": "quant-ph/0311127",
"authors": [
"Detlef Duerr",
"Sheldon Goldstein",
"Roderich Tumulka",
"Nino Zanghi"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s10701-004-1983-9",
"journal_ref": "Foundations of Physics 35(3): 449-467 (2005)",
"title": "On the Role of Density Matrices in Bohmian Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0311127"
},
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