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The noncommutative degenerate electron gas
F. S. Bemfica, H. O. Girotti
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0506191
- categories:
- quant-ph hep-th
- comments:
- 11 pages, to appear in J. Phys. A: Math. Gen
- doi:
- 10.1088/0305-4470/38/30/L01
- arxiv_id:
- quant-ph/0506191
- journal_ref:
- J.Phys. A38 (2005) L539
- created:
- 2005-06-22
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