Spectrum for quantum duffing oscillator and small‐divisor equation with large‐variable coefficient

By establishing a new estimate of the solutions for the small‐divisor equation with large variable coefficients and using the KAM technique, we prove a reduction theorem that entails the pure point nature of the Floquet spectrum of the quantum Duffing oscillator with a small perturbation temporal quasi‐periodic with nonresonant frequencies. © 2010 Wiley Periodicals, Inc.