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Exactly solvable model of superconducting magnetic alloys

Published Jan 1, 2008• 0 citations

Abstract

A model describing the Anderson impurity in the Bardeen-Cooper-Schriffer superconductor is proven to exhibit hidden integrability and is diagonalized exactly by the Bethe ansatz. Typeset using REVTEX 1 The basic theoretical models describing magnetic impurities in nonmagnetic normal metals, such as the s-d (Kondo) model, the Anderson model, etc., are integrable under two additional conditions [1]: (i) an electron-impurity coupling is assumed to be energy independent, and (ii) a band electron dispersion ε(k) can be linearized around the Fermi level, ε(k) ≃ vF(k − kF), where kF and vF are the Fermi momentum and velocity, respectively. Only under these conditions, both an electron-impurity scattering and an effective electronelectron coupling are described in terms of discontinuous jumps in the Bethe ansatz wave functions. Therefore a linear dispersion of particles and a pointlike particle-impurity coupling are considered now as the necessary mathematical conditions for integrability of the “impurity ” models. Because a carrier dispersion in superconducting metals cannot be linearized,

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A model describing the Anderson impurity in the Bardeen-Cooper-Schriffer superconductor is proven to exhibit hidden integrability and is diagonalized exactly by the Bethe ansatz. Typeset using REVTEX 1 The basic theoretical models describing magnetic impurities in nonmagnetic normal metals, such as the s-d (Kondo) model, the Anderson model, etc., are integrable under two additional conditions [1]: (i) an electron-impurity coupling is assumed to be energy independent, and (ii) a band electron dispersion ε(k) can be linearized around the Fermi level, ε(k) ≃ vF(k − kF), where kF and vF are the Fermi momentum and velocity, respectively. Only under these conditions, both an electron-impurity scattering and an effective electronelectron coupling are described in terms of discontinuous jumps in the Bethe ansatz wave functions. Therefore a linear dispersion of particles and a pointlike particle-impurity coupling are considered now as the necessary mathematical conditions for integrability of the “impurity ” models. Because a carrier dispersion in superconducting metals cannot be linearized,

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