FM 2003-04 (mp_arc 03-203)

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