27 citations · 65 across the 12 of their papers we have counts for
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Generalized Reducibility and Growth of Sobolev Norms
Zhenguo Liang, Zhiyan Zhao
We introduce the concept of {\it generalized reducibility}, which provides a flexible framework for analyzing the long-time behavior of solutions to quadratic quantum Hamiltonians.…
Symplectic Normal Form and Growth of Sobolev Norm
Zhenguo Liang, Jiawen Luo, Zhiyan Zhao
For a class of reducible Hamiltonian partial differential equations (PDEs) with arbitrary spatial dimensions, quantified by a quadratic polynomial with time-dependent coefficients,…
Reducibility of 1-D quantum harmonic oscillator with new unbounded oscillatory perturbations
Jin Xu, Jiawen Luo, Zhiqiang Wang +1
Enlightened by Lemma 1.7 in \cite{LiangLuo2021}, we prove a similar lemma which is based upon oscillatory integrals and Langer's turning point theory. From it we show that the Schr…
Almost reducibility and oscillatory growth of Sobolev norms
Zhenguo Liang, Zhiyan Zhao, Qi Zhou
For 1D quantum harmonic oscillator perturbed by a time quasi-periodic quadratic form of , we show its almost reducibility. The growth of Sobolev norms of so…
Growth of Sobolev Norms in 1-d Quantum Harmonic Oscillator with Polynomial Time Quasi-periodic Perturbation
Jiawen Luo, Zhenguo Liang, Zhiyan Zhao
We consider the one-dimensional quantum harmonic oscillator perturbed by a linear operator which is a polynomial of degree in , with coefficients quasi-…
1-d Quantum Harmonic Oscillator with Time Quasi-periodic Quadratic Perturbation: Reducibility and Growth of Sobolev Norms
Zhenguo Liang, Zhiyan Zhao, Qi Zhou
For a family of 1-d quantum harmonic oscillator with a perturbation which is parametrized by and quadratic on and w…