dorsal/arxiv
View SchemaThe noncommutative degenerate electron gas
| Authors | F. S. Bemfica, H. O. Girotti |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506191 |
| URL | https://arxiv.org/abs/quant-ph/0506191 |
| DOI | 10.1088/0305-4470/38/30/L01 |
| Journal | J.Phys. A38 (2005) L539 |
Abstract
The quantum dynamics of nonrelativistic single particle systems involving noncommutative coordinates, usually referred to as noncommutative quantum mechanics, has lately been the object of several investigations. In this note we pursue these studies for the case of multi-particle systems. We use as a prototype the degenerate electron gas whose dynamics is well known in the commutative limit. Our central aim here is to understand qualitatively, rather than quantitatively, the main modifications induced by the presence of noncommutative coordinates. We shall first see that the noncommutativity modifies the exchange correlation energy while preserving the electric neutrality of the model. By employing time-independent perturbation theory together with the Seiberg-Witten map we show, afterwards, that the ionization potential is modified by the noncommutativity. It also turns out that the noncommutative parameter acts as a reference temperature. Hence, the noncommutativity lifts the degeneracy of the zero temperature electron gas.
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"abstract": "The quantum dynamics of nonrelativistic single particle systems involving\nnoncommutative coordinates, usually referred to as noncommutative quantum\nmechanics, has lately been the object of several investigations. In this note\nwe pursue these studies for the case of multi-particle systems. We use as a\nprototype the degenerate electron gas whose dynamics is well known in the\ncommutative limit. Our central aim here is to understand qualitatively, rather\nthan quantitatively, the main modifications induced by the presence of\nnoncommutative coordinates. We shall first see that the noncommutativity\nmodifies the exchange correlation energy while preserving the electric\nneutrality of the model. By employing time-independent perturbation theory\ntogether with the Seiberg-Witten map we show, afterwards, that the ionization\npotential is modified by the noncommutativity. It also turns out that the\nnoncommutative parameter acts as a reference temperature. Hence, the\nnoncommutativity lifts the degeneracy of the zero temperature electron gas.",
"arxiv_id": "quant-ph/0506191",
"authors": [
"F. S. Bemfica",
"H. O. Girotti"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1088/0305-4470/38/30/L01",
"journal_ref": "J.Phys. A38 (2005) L539",
"title": "The noncommutative degenerate electron gas",
"url": "https://arxiv.org/abs/quant-ph/0506191"
},
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