4 papers
Ballistic Transport for Discrete Multi-Dimensional Schrödinger Operators With Decaying Potential
David Damanik, Zhiyan Zhao
We consider the discrete Schrödinger operator on with a decaying potential, in arbitrary lattice dimension , where is th…
Long-time stability for nonlinear Maryland models
Ruijie Cui, Zhiyan Zhao
For the dimensional nonlinear Maryland model \begin{equation}\label{eq-abs} \ri\partial_t q_n=\tanÏ(n\cdot\varpi+x)q_n+ε(Îq)_n+|q_n|^2q_n,\quad n\in{\Z^d}, \end{equation} wi…
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,…