Geodesic
Elementary excitations in the Anderson--Hubbard model
Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 3, pp. 425-430

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The dispersion Iaw of long-wavelength spin-wave Bose excitations in a paramagnetic metal described by the Hubbard model is obtained from the equation for the scattering amplitude of electrons and holes with opposite spins. The effective exchange interaction that determines the behavior of these excitations is expressed in terms of the parameters of the model. 
@article{TMF_1981_47_3_a13,
     author = {A. V. Vedyaev and V. A. Ivanov},
     title = {Elementary excitations in the {Anderson--Hubbard} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {425--430},
     publisher = {mathdoc},
     volume = {47},
     number = {3},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1981_47_3_a13/}
}
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A. V. Vedyaev; V. A. Ivanov. Elementary excitations in the Anderson--Hubbard model. Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 3, pp. 425-430. http://geodesic.mathdoc.fr/item/TMF_1981_47_3_a13/