Search for content and authors 
Quantum statistics and discreteness. Differences between the canonical and grand canonical ensembles for a fermionic lattice gas 
Ryszard Kutner ^{1}, Radosław Przeniosło ^{1}, Maciej Kwiatkowski ^{2} 
1. Faculty of Physics, University of Warsaw (FPUW), Pasteura 5, Warsaw 02093, Poland 
Abstract 
Studying the electronic properties of small metallic particles Kubo and subsequently Denton, Mühlschlegel and Scalapino recognized the surprising effect that the mean occupation numbers of noninteracting fermions (electrons) are not given within the canonical ensemble by the usual expression of FermiDirac statistics. The fermions behave as if they are colder and observed deviations are most significant in the vicinity of the Fermi level. The results of our Monte Carlo simulations, as well as our complementary numerical and analytical results are in very good agreement with the predictions of Denton et al. We found that the effect vanishes for very small and very large spacing between the energy levels in comparison to the thermal energy k_{B}T. Associated with this effect are the particlehole correlations. Extending the method used by Denton et al. we derive an analytical formula for the particlehole correlation functions whose predictions are again in very good agreement with our numerical results. The lowtemperature aspects of the effect are considered by applying a twostate model. The role of the finitesize effect is also discussed.
Annalen der Physik 507 (1995), 646. 
Legal notice 

Related papers 
Presentation: Article at Econophysics group of Ryszard Kutner, by Ryszard Kutner Submitted: 20160329 14:43 Revised: 20160329 14:43 