Reducibility for Schrödinger Operator with Finite Smooth and Time-Quasi-periodic Potential

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.

Keywords

Reducibility / Quasi-periodic Schrödinger operator / KAM theory / Finite smooth potential / Lyapunov exponent / Pure-Point spectrum