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20182023
most citedGrowth of Sobolev Norms in 1-d Quantum Harmonic Oscillator with Polynomial Time Quasi-periodic Perturbation

11 citations · 23 across the 5 of their papers we have counts for

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math.AP2023★ 1 cited

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,…

math.AP2023

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…

math.AP2021★ 11 cited

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-…