**Author:**
Guido Gentile

**Title:** *
Pure point spectrum for two-level systems
in a strong quasi-periodic field
*

**Abstract: **
We consider two-level atoms in a strong external quasi-periodic
field with Diophantine frequency vector. We show that if the field is
an analytic function with zero average, then for a large set of
values of its frequency vector, characterized by imposing
infinitely many Diophantine conditions, the spectrum of the
quasi-energy operator is pure point, as in the case of
non-zero average which was already known in literature.

**Keywords:**
Two-level systems, pure point spectrum, generalized Riccati equation,
small divisors, quasi-periodic solutions, trees, multiscale analysis,
resummation of divergent series, Cantor set

Guido Gentile

Dipartimento di Matematica

Universita` di Roma Tre

Largo San Leonardo Murialdo 1, 00146 Roma, Italy

e-mail: gentile@mat.uniroma3.it