dorsal/arxiv
View SchemaNon-positivity of Groenewold operators
| Authors | A. J. Bracken, J. G. Wood |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407052 |
| URL | https://arxiv.org/abs/quant-ph/0407052 |
| DOI | 10.1209/epl/i2004-10175-8 |
| Journal | Europhys. Lett., 68 (1) pp. 1-7 (2004) |
Abstract
A central feature in the Hilbert space formulation of classical mechanics is the quantisation of classical Liouville densities, leading to what may be termed term Groenewold operators. We investigate the spectra of the Groenewold operators that correspond to Gaussian and to certain uniform Liouville densities. We show that when the classical coordinate-momentum uncertainty product falls below Heisenberg's limit, the Groenewold operators in the Gaussian case develop negative eigenvalues and eigenvalues larger than 1. However, in the uniform case, negative eigenvalues are shown to persist for arbitrarily large values of the classical uncertainty product.
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"abstract": "A central feature in the Hilbert space formulation of classical mechanics is\nthe quantisation of classical Liouville densities, leading to what may be\ntermed term Groenewold operators. We investigate the spectra of the Groenewold\noperators that correspond to Gaussian and to certain uniform Liouville\ndensities. We show that when the classical coordinate-momentum uncertainty\nproduct falls below Heisenberg\u0027s limit, the Groenewold operators in the\nGaussian case develop negative eigenvalues and eigenvalues larger than 1.\nHowever, in the uniform case, negative eigenvalues are shown to persist for\narbitrarily large values of the classical uncertainty product.",
"arxiv_id": "quant-ph/0407052",
"authors": [
"A. J. Bracken",
"J. G. Wood"
],
"categories": [
"quant-ph"
],
"doi": "10.1209/epl/i2004-10175-8",
"journal_ref": "Europhys. Lett., 68 (1) pp. 1-7 (2004)",
"title": "Non-positivity of Groenewold operators",
"url": "https://arxiv.org/abs/quant-ph/0407052"
},
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