Abstract
For the integrable generalized model of superconductivity, the solution of the Richardson equations is studied for a model spectrum. For the case of a narrow band, the solution is presented in terms of generalized Laguerre or Jacobi polynomials. In the asymptotic limit, when the Richardson equations are transformed into a singular integral equation, the properties of the integration contour are discussed and the spectral density is calculated. The conditions of appearance of gaps in the spectrum are investigated.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 3, pp. 314–326, March, 2007.
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Belokolos, E.D. Integrable superconductivity and Richardson equations. Ukr Math J 59, 343–360 (2007). https://doi.org/10.1007/s11253-007-0022-3
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DOI: https://doi.org/10.1007/s11253-007-0022-3