The distribution of electrons in small one-dimensional systems is obtained under the assumption of evenly spaced energy levels. The method consists of considering isolated systems and shifting electrons from their zero-temperature location. The distribution is then expressed in terms of the number of partitions of integers. When the system is in thermal contact with an electrical insulator, the electron distribution is obtained by averaging the previous result with the Boltzmann factor as a weight. Finally, when the system is in thermal and electrical contact with a large medium, the Fermi–Dirac distribution emerges through averaging over the number N of electrons. The statistics of light emitted or absorbed by the electron gas is obtained without quantization of the optical field. Our rigorous though elementary treatment helps clarify concepts employed in statistical mechanics.
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March 1999
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March 01 1999
Illustration of the Fermi–Dirac statistics
J. Arnaud;
J. Arnaud
Mas Liron, Saint-Martial, F 30440, France
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J. M. Boé;
J. M. Boé
Département de Mathématiques et Informatique Appliquées, Univ. Paul Valéry, F 34199 Montpellier Cédex 5, France
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L. Chusseau;
L. Chusseau
Centre d’Electronique et de Micro-optoélectronique de Montpellier, Unité Mixte de Recherche CNRS-Université No. 5507, Université de Montpellier II, F 34095 Montpellier Cédex 5, France
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F. Philippe
F. Philippe
Département de Mathématiques et Informatique Appliquées, Univ. Paul Valéry, F 34199 Montpellier Cédex 5, France
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Am. J. Phys. 67, 215–221 (1999)
Article history
Received:
April 30 1998
Accepted:
August 02 1998
Citation
J. Arnaud, J. M. Boé, L. Chusseau, F. Philippe; Illustration of the Fermi–Dirac statistics. Am. J. Phys. 1 March 1999; 67 (3): 215–221. https://doi.org/10.1119/1.19228
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