- 02-478 Guido Gentile
- Quasi-periodic solutions for two-level systems
Nov 22, 02
(auto. generated ps),
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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.