dorsal/arxiv
View SchemaOn the goodness of "quantum blobs" in phase space quantization
| Authors | Maurice de Gosson |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407129 |
| URL | https://arxiv.org/abs/quant-ph/0407129 |
Abstract
We replace the usual notion of quantum cell from statistical mechanics by that of "quantum blob". A quantum blob is the transform, by a linaer symplectic transformation, of a phase space ball with radius equal to the square root of h-bar. The intersection of a quantum blob with any symplectic plane is an ellipse with area one half of h. This very special property, which is closed related to the principle of the symplectic camel, leads to a symplectic invariant statement of the uncertainty principle. We moreover prove that the average of a phase space Gaussian over a quantum blob is the Wigner transform of a minimum uncertainty Gaussian.
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"abstract": "We replace the usual notion of quantum cell from statistical mechanics by\nthat of \"quantum blob\". A quantum blob is the transform, by a linaer symplectic\ntransformation, of a phase space ball with radius equal to the square root of\nh-bar. The intersection of a quantum blob with any symplectic plane is an\nellipse with area one half of h. This very special property, which is closed\nrelated to the principle of the symplectic camel, leads to a symplectic\ninvariant statement of the uncertainty principle. We moreover prove that the\naverage of a phase space Gaussian over a quantum blob is the Wigner transform\nof a minimum uncertainty Gaussian.",
"arxiv_id": "quant-ph/0407129",
"authors": [
"Maurice de Gosson"
],
"categories": [
"quant-ph"
],
"title": "On the goodness of \"quantum blobs\" in phase space quantization",
"url": "https://arxiv.org/abs/quant-ph/0407129"
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