2005/06/22 by F. S. Bemfica, F S Bemfica, H. O. Girotti +1
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #hep-th #quant-ph
paper · pdf · doi:10.1088/0305-4470/38/30/l01
published as J.Phys. A38 (2005) L539 · 11 pages, to appear in J. Phys. A: Math. Gen
arxiv created 2005/06/22 · openalex publication_date 2005/07/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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 letter 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.