On the N-exciton normalization factor

• Published in: The European physical journal. B, Condensed matter physics Vol. 31; no. 1; pp. 17 - 24
• Main Authors: COMBESCOT, M, LEYRONAS, X, TANGUY, C
• Format: Journal Article
• Language: English
• Published: Les Ulis Springer 2003; Berlin EDP sciences; Springer-Verlag
• Subjects: Collective effects (Bose effects, phase space filling, and excitonic phase transitions); Condensed matter: electronic structure, electrical, magnetic, and optical properties; Electron states; Exact sciences and technology; Excitons and related phenomena; Physics; Excitons; Ground states; Superconductivity model; Standardization; Theoretical study; N-body problems; Coulomb interaction; Recursion relations; BCS theory
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2003-00003-1

The N-ground-state-exciton normalization factor, namely , with the exact ground state exciton creation operator, differs from N! because the excitons are not perfect bosons. The quantity FN turns out to be crucial for problems dealing with interacting excitons. Indeed, the excitons feel each other not only through the Coulomb interaction but also through Pauli exclusion between their components. A quite novel purely Pauli contribution exists in their many-body effects, which relies directly on FN. Following procedures used in the commutation technique we recently introduced to treat interacting close-to-bosons, and in the BCS theory of superconductivity, we rederive important relations verified by the FN's. We also give new explicit expressions of FN valid for small but large, as FN does not read in terms of but , the exciton number N being possibly huge in macroscopic samples. Due to this superextensivity, FN does not appear alone in physical quantities, but through ratios like FN+p/FN. We end this work by giving the expansion of these ratios, useful for all purely Pauli many-body effects.