dorsal/arxiv
View SchemaOn the precise connection between the GRW master-equation and master-equations for the description of decoherence
| Authors | B. Vacchini |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0701218 |
| URL | https://arxiv.org/abs/quant-ph/0701218 |
| DOI | 10.1088/1751-8113/40/10/015 |
| Journal | J. Phys. A: Math. Theor. 40 (2007) 2463-2473 |
Abstract
We point out that the celebrated GRW master-equation is invariant under translations, reflecting the homogeneity of space, thus providing a particular realization of a general class of translation-covariant Markovian master-equations. Such master-equations are typically used for the description of decoherence due to momentum transfers between system and environment. Building on this analogy we show the exact relationship between the GRW master-equation and decoherence master-equations, further providing a collisional decoherence model formally equivalent to the GRW master-equation. This allows for a direct comparison of order of magnitudes of relevant parameters. This formal analogy should not lead to confusion on the utterly different spirit of the two research fields, in particular it has to be stressed that the decoherence approach does not lead to a solution of the measurement problem. Building on this analogy however the feasibility of the extension of spontaneous localization models in order to avoid the infinite energy growth is discussed. Apart from a particular case considered in the paper, it appears that the amplification mechanism is generally spoiled by such modifications.
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"abstract": "We point out that the celebrated GRW master-equation is invariant under\ntranslations, reflecting the homogeneity of space, thus providing a particular\nrealization of a general class of translation-covariant Markovian\nmaster-equations. Such master-equations are typically used for the description\nof decoherence due to momentum transfers between system and environment.\nBuilding on this analogy we show the exact relationship between the GRW\nmaster-equation and decoherence master-equations, further providing a\ncollisional decoherence model formally equivalent to the GRW master-equation.\nThis allows for a direct comparison of order of magnitudes of relevant\nparameters. This formal analogy should not lead to confusion on the utterly\ndifferent spirit of the two research fields, in particular it has to be\nstressed that the decoherence approach does not lead to a solution of the\nmeasurement problem. Building on this analogy however the feasibility of the\nextension of spontaneous localization models in order to avoid the infinite\nenergy growth is discussed. Apart from a particular case considered in the\npaper, it appears that the amplification mechanism is generally spoiled by such\nmodifications.",
"arxiv_id": "quant-ph/0701218",
"authors": [
"B. Vacchini"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1751-8113/40/10/015",
"journal_ref": "J. Phys. A: Math. Theor. 40 (2007) 2463-2473",
"title": "On the precise connection between the GRW master-equation and master-equations for the description of decoherence",
"url": "https://arxiv.org/abs/quant-ph/0701218"
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