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Développements asymptotiques des perturbations lentes de l’opérateur de Schrödinger periodique. (Asymptotic expansion for slow perturbations of the periodic Schrödinger operator). (French) Zbl 0779.35076

Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math., Palaiseau 1991-1992, No.X, 11 p. (1992).
The author uses a theory of reduction due to Gérard-Martinez- Sjöstrand, to obtain a full asymptotic expansion of partial traces associated to slowly varying perturbations of the periodic Schrödinger operator. Here the perturbation consists of an electromagnetic field. Moreover, under an assumption of non-degeneracy of the Floquet spectral band corresponding to the energy cut-off, it is stated that the second term of the asymptotics vanishes.

MSC:

35P20 Asymptotic distributions of eigenvalues in context of PDEs
35S05 Pseudodifferential operators as generalizations of partial differential operators
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
Full Text: EuDML