Author: Guido Gentile
Quasi-periodic solutions for two-level systems
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.
Keywords: Two-level systems, generalized Riccati equation, quasi-periodic solutions, trees, resummation of divergent series, Cantor set
Dipartimento di Matematica
Universita` di Roma Tre
Largo San Leonardo Murialdo 1, 00146 Roma, Italy