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| Reducibility for Schr\"{o}dinger Operator with Finite Smooth and Time-Quasi-periodic Potential |
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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 |
| Page view： 448
Net amount： 861 |
Authors： |
Jing LI; |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11601277, 11771253). |
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| 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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