27 citations · 65 across the 12 of their papers we have counts for
12 papers
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…
Reducibility of 1-D Quantum Harmonic Oscillator with Decaying Conditions on the Derivative of Perturbation Potentials
Zhenguo Liang, Zhiqiang Wang
We prove the reducibility of 1-D quantum harmonic oscillators in perturbed by a quasi-periodic in time potential under the following conditions, namely there…
Reducibility of Quantum Harmonic Oscillator on Perturbed by a Quasi-periodic Potential with Logarithmic Decay
Zhenguo Liang, Zhiqiang Wang
We prove the reducibility of quantum harmonic oscillators in perturbed by a quasi-periodic in time potential with . By a new est…
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…
Reducibility of 1-d Quantum Harmonic Oscillator Equation with Unbounded Oscillation Perturbations
Zhenguo Liang, Jiawen Luo
We build a new estimate relative with Hermite functions based upon oscillatory integrals and Langer's turning point theory. From it we show that the equation $$ i \partial_t u =-\p…
Perfect Seismic Wave Absorbers for the 8th Magnitude Earthquakes
Liang Sun, Feilong Xu, Zhen Liang +2
Most modern buildings and infrastructures are not designed to resist 8th magnitude earthquakes, for which studies on phononic crystals and local resonators reported so far are not…
Reducibility of quantum harmonic oscillator on with differential and quasi-periodic in time potential
Zhenguo Liang, Zhiguo Wang
We improve the results by Grébert and Paturel in \cite{GP} and prove that a linear Schrödinger equation on with harmonic potential and small -quasiperiodic potenti…
1d Quantum Harmonic Oscillator Perturbed by a Potential with Logarithmic Decay
Zhiguo Wang, Zhenguo Liang
In this paper we prove an infinite dimensional KAM theorem, in which the assumptions on the derivatives of perturbation in \cite{GT} are weakened from polynomial decay to logarithm…