2011/12/07 by J N Kriel, Johannes N. Kriel, F. G. Scholtz +1
Mathematics · Physics and Astronomy · #Angular momentum #Black Holes and Theoretical Physics #Classical mechanics #Commutative property #Cosmology and Gravitation Theories #Entropy (arrow of time) #Fermion #Geometry #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Scaling #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/45/9/095301
15 pages, 10 figures
arxiv created 2011/12/07 · openalex publication_date 2012/02/16 · arxiv updated 2015/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the properties of two- and three-dimensional non-commutative fermion gases with fixed total z-component of angular momentum, J \n z, and at high density for the simplest form of non-commutativity involving constant spatial commutators. Analytic expressions for the entropy and pressure are found. The entropy exhibits non-extensive behaviour, while the pressure reveals the presence of incompressibility in two, but not in three dimensions. Remarkably, for two-dimensional systems close to the incompressible density, the entropy is proportional to the square root of the system size, i.e. for such systems the number of microscopic degrees of freedom is determined by the circumference rather than the area (size) of the system. The absence of incompressibility in three dimensions, and subsequently also the absence of a scaling law for the entropy analogous to the one found in two dimensions, is attributed to the form of the non-commutativity used here, the breaking of the rotational symmetry it implies and the subsequent constraint on J \n z rather than the angular momentum J. Restoring the rotational symmetry while constraining the total angular momentum J seems to be crucial for incompressibility in three dimensions. We briefly discuss ways in which this may be done and point out possible obstacles. © 2012 IOP Publishing Ltd.