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Communications in Mathematical Physics

, Volume 242, Issue 1–2, pp 221–250 | Cite as

Quasi-Periodic Solutions for Two-Level Systems

  • Guido Gentile
Article

Abstract

We consider the Schrödinger equation for a class of two-level atoms in a quasi-periodic external field in the case in which the spacing 2ɛ between the two unperturbed energy levels is small, and we study the problem of finding quasi-periodic solutions of a related generalized Riccati equation. We prove the existence of quasi-periodic solutions of the latter equation for a Cantor set ℰ of values of ɛ 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

Energy Level Power Series Lebesgue Measure External Field Riccati Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Guido Gentile
    • 1
  1. 1.Dipartimento di MatematicaUniversità di Roma TreRomaItaly

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