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APS

Quantum Statistics of Nuclei, Atoms and Cooper Pairs (Pairons).

Shigeji Fujita, S. P. Gau, Salvador Godoy

Published Apr 1, 1997• 0 citations
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We show that the eigenvalues of the number operator [Formula: see text] in the pair state (k1, k2), where c's and c†'s are fermion operators, are limited to 0 or 1, while the eigenvalues of the pair-number operator with the net momentum q≡ k1+k2 fixed, [Formula: see text], are 0, 1, 2,…. Both fermionic and bosonic natures of the Cooper pairs (pairons) must be used in the superconductivity theory. The Bose–Einstein condensation (BEC) of the pairons moving with a linear energy–momentum relation occurs at [Formula: see text] (3D), [Formula: see text] (2D), where n0 is the pairon density and v F the Fermi velocity. The connection between this [Formula: see text] and the BCS superconducting temperature is discussed.

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Basics of Quantum Statistics

Walter Greiner

Springer eBooks•Jan 1, 1998•0 citations
Abstract The Cooper pair has the total spin S = 0. So, in accordance with the Pauli principle, the wave functions describing the Cooper pair system should have the boson permutation symmetry, but the pairon operators (Cooper's pair operators) do not obey the boson commutation relations. The pairon operators may not be considered neither as the Bose operators, nor as the Fermi operators. In this work, we analyze the statistical properties and the commutation relations for the pairon operator and reveal that they correspond to the modified parafermi statistics of rank p = 1. Two different expressions for the Cooper pair number operator are presented. We demonstrate that the calculations with a Hamiltonian expressed via pairon operators is more convenient using the commutation properties of these operators without presenting them as a product of fermion operators. This allows to study problems in which the interactions between Cooper's pair are also included. The problem of two interacting Cooper's pairs is discussed. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We show that the eigenvalues of the number operator [Formula: see text] in the pair state (k1, k2), where c's and c†'s are fermion operators, are limited to 0 or 1, while the eigenvalues of the pair-number operator with the net momentum q≡ k1+k2 fixed, [Formula: see text], are 0, 1, 2,…. Both fermionic and bosonic natures of the Cooper pairs (pairons) must be used in the superconductivity theory. The Bose–Einstein condensation (BEC) of the pairons moving with a linear energy–momentum relation occurs at [Formula: see text] (3D), [Formula: see text] (2D), where n0 is the pairon density and v F the Fermi velocity. The connection between this [Formula: see text] and the BCS superconducting temperature is discussed.