02-478 Guido Gentile

Quasi-periodic solutions for two-level systems (414K, postscript) Nov 22, 02

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Abstract. We consider the Schroedinger equation for a class of two-level atoms in a quasi-periodic external field in the case in which the spacing 2e between the two unperturbed energy levels is small. We prove the existence of quasi-periodic solutions for a Cantor set E of values of e around the origin which is of positive Lebesgue measure: such solutions can be obtained from the formal power series by a suitable resummation procedure. The set E can be characterized by requesting infinitely many Diophantine conditions of Mel'nikov type.

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