Reducibility for Schr\"{o}dinger Operator with Finite Smooth and Time-Quasi-periodic Potential

Citation:

Jing LI.Reducibility for Schr\"{o}dinger Operator with Finite Smooth and Time-Quasi-periodic Potential[J].Chinese Annals of Mathematics B,2020,41(3):419~440
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Authors:

Jing LI;

Foundation:

This work was supported by the National Natural Science Foundation of China (Nos.11601277, 11771253).
Abstract: In this paper, the author establishes a reduction theorem for linear Schr\"odinger 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 Schr\"odinger operator possesses the property of pure point spectra and zero Lyapunov exponent.

Keywords:

Reducibility, Quasi-periodic Schr"odinger operator, KAM theory, Finite smooth potential, Lyapunov exponent, Pure-Point spectrum

Classification:

35P05, 37K55, 81Q15
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