Abstract
In this paper, the author establishes a reduction theorem for linear Schrödinger equation with finite smooth and time-quasi-periodic potential subject to Dirichlet boundary condition by means of KAM (Kolmogorov-Arnold-Moser) technique. Moreover, it is proved that the corresponding Schrödinger operator possesses the property of pure point spectra and zero Lyapunov exponent.
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The author is grateful to anonymous referee for his/her valuable comments, which greatly improve the original manuscript of this paper.
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This work was supported by the National Natural Science Foundation of China (Nos. 11601277, 11771253).
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Li, J. Reducibility for Schrödinger Operator with Finite Smooth and Time-Quasi-periodic Potential. Chin. Ann. Math. Ser. B 41, 419–440 (2020). https://doi.org/10.1007/s11401-020-0208-7
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DOI: https://doi.org/10.1007/s11401-020-0208-7
Keywords
- Reducibility
- Quasi-periodic Schrödinger operator
- KAM theory
- Finite smooth potential
- Lyapunov exponent
- Pure-Point spectrum