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 qu...

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Veröffentlicht in:	Communications on pure and applied mathematics 2010-09, Vol.63 (9), p.1145-1172
Hauptverfasser:	Liu, Jianjun, Yuan, Xiaoping
Format:	Artikel
Sprache:	eng
Schlagworte:	Differential equations Estimating techniques Exact sciences and technology General mathematics General, history and biography Mathematical analysis Mathematics Operator theory Oscillators Quantum theory Sciences and techniques of general use Spectrum analysis Variables
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Zusammenfassung:	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.
ISSN:	0010-3640 1097-0312
DOI:	10.1002/cpa.20314