Summary
The distribution of the number of particles in the BCS state is studied. It is shown to possess only one maximum. The binomial distribution, which corresponds to the degenerate model of the Pairing Force, appears to have remarkable extremum properties. The binomial distribution approximating the best any given BCS distribution is derived. The limit of infinite systems is discussed. It is shown that, for symmetrical systems, for systems with near-lying individual states, and for infinite systems, the most probable value of the number of particles is the average value.
Riassunto
Si studia la distribuzione del numero di particelle nello stato BCS. Si dimostra che possiede un solo massimo. La distribuzione binomiale che corrisponde al modello degenerato della forza d’accoppiamento appare possedere notevoli proprietà estremanti. Si dériva la distribuzione binomiale che approssima la miglior distribuzione di BCS flnora data. Si discute il limite dei sistemi inflniti. Si dimostra che per sistemi simmetrici, per sistemi con stati indivisuali adiacenti e per sistemi inflniti il più probabile valore del numero di particelle è il valor medio.
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On leave from Laboratoire de Physique Théorique, Institut du Eadium, Orsay.
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Høgaasen, J. A study of the Bardeen-Cooper-Schrieffer distribution. Nuovo Cim 36, 773–787 (1965). https://doi.org/10.1007/BF02749780
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DOI: https://doi.org/10.1007/BF02749780