dorsal/arxiv
View SchemaAssumptions that imply quantum dynamics is linear
| Authors | Thomas F. Jordan |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0508092 |
| URL | https://arxiv.org/abs/quant-ph/0508092 |
| DOI | 10.1103/PhysRevA.73.022101 |
| Journal | Phys. Rev. A 73, 022101 (2006) |
Abstract
A basic linearity of quantum dynamics, that density matrices are mapped linearly to density matrices, is proved very simply for a system that does not interact with anything else. It is assumed that at each time the physical quantities and states are described by the usual linear structures of quantum mechanics. Beyond that, the proof assumes only that the dynamics does not depend on anything outside the system but must allow the system to be described as part of a larger system. The basic linearity is linked with previously established results to complete a simple derivation of the linear Schrodinger equation. For this it is assumed that density matrices are mapped one-to-one onto density matrices. An alternative is to assume that pure states are mapped one-to-one onto pure states and that entropy does not decrease.
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"abstract": "A basic linearity of quantum dynamics, that density matrices are mapped\nlinearly to density matrices, is proved very simply for a system that does not\ninteract with anything else. It is assumed that at each time the physical\nquantities and states are described by the usual linear structures of quantum\nmechanics. Beyond that, the proof assumes only that the dynamics does not\ndepend on anything outside the system but must allow the system to be described\nas part of a larger system. The basic linearity is linked with previously\nestablished results to complete a simple derivation of the linear Schrodinger\nequation. For this it is assumed that density matrices are mapped one-to-one\nonto density matrices. An alternative is to assume that pure states are mapped\none-to-one onto pure states and that entropy does not decrease.",
"arxiv_id": "quant-ph/0508092",
"authors": [
"Thomas F. Jordan"
],
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"quant-ph"
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"doi": "10.1103/PhysRevA.73.022101",
"journal_ref": "Phys. Rev. A 73, 022101 (2006)",
"title": "Assumptions that imply quantum dynamics is linear",
"url": "https://arxiv.org/abs/quant-ph/0508092"
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