dorsal/arxiv
View SchemaJaynes-Cummings Model and a Non-Commutative "Geometry" : A Few Problems Noted
| Authors | Kazuyuki Fujii |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0410201 |
| URL | https://arxiv.org/abs/quant-ph/0410201 |
Abstract
In this paper we point out that the Jaynes-Cummings model without taking a renonance conditon gives a non-commutative version of the simple spin model (including the parameters $x$, $y$ and $z$) treated by M. V. Berry. This model is different from usual non-commutative ones because the x-y coordinates are quantized, while the z coordinate is not. One of new and interesting points in our non-commutative model is that the strings corresponding to Dirac ones in the Berry model exist only in states containing the ground state (${\cal F}\times \{\ket{0}\} \cup \{\ket{0}\}\times {\cal F}$), while for other excited states (${\cal F}\times {\cal F} \setminus {\cal F}\times \{\ket{0}\} \cup \{\ket{0}\}\times {\cal F}$) they don't exist. It is probable that a non-commutative model makes singular objects (singular points or singular lines or etc) in the corresponding classical model mild or removes them partly.
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"abstract": "In this paper we point out that the Jaynes-Cummings model without taking a\nrenonance conditon gives a non-commutative version of the simple spin model\n(including the parameters $x$, $y$ and $z$) treated by M. V. Berry. This model\nis different from usual non-commutative ones because the x-y coordinates are\nquantized, while the z coordinate is not.\n One of new and interesting points in our non-commutative model is that the\nstrings corresponding to Dirac ones in the Berry model exist only in states\ncontaining the ground state (${\\cal F}\\times \\{\\ket{0}\\} \\cup \\{\\ket{0}\\}\\times\n{\\cal F}$), while for other excited states (${\\cal F}\\times {\\cal F} \\setminus\n{\\cal F}\\times \\{\\ket{0}\\} \\cup \\{\\ket{0}\\}\\times {\\cal F}$) they don\u0027t exist.\n It is probable that a non-commutative model makes singular objects (singular\npoints or singular lines or etc) in the corresponding classical model mild or\nremoves them partly.",
"arxiv_id": "quant-ph/0410201",
"authors": [
"Kazuyuki Fujii"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"title": "Jaynes-Cummings Model and a Non-Commutative \"Geometry\" : A Few Problems Noted",
"url": "https://arxiv.org/abs/quant-ph/0410201"
},
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