Guido Gentile
Quasi-periodic solutions for two-level systems
(414K, postscript)

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.