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Spectrum for quantum duffing oscillator and small‐divisor equation with large‐variable coefficient
Author(s) -
Liu Jianjun,
Yuan Xiaoping
Publication year - 2010
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20314
Subject(s) - mathematics , duffing equation , divisor (algebraic geometry) , quantum , floquet theory , spectrum (functional analysis) , perturbation (astronomy) , mathematical analysis , variable (mathematics) , quantum mechanics , pure mathematics , physics , nonlinear system
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.