KAM for high-dimensional nonlinear quantum harmonic oscillator
Analysis of PDEs
2024-07-30 v1 Dynamical Systems
Abstract
In this paper, we study high-dimensional nonlinear quantum harmonic oscillator equation. We show the equation admits many time quasi-periodic solutions by establishing an abstract infinite dimensional KAM theorem with multiple normal frequencies. The proof is based on the classical KAM scheme, and the key is a decaying structure of Hessian matrices of Hamiltonian functions.
Keywords
Cite
@article{arxiv.2407.19312,
title = {KAM for high-dimensional nonlinear quantum harmonic oscillator},
author = {Jianjun Liu and Caihong Qi and Guanghua Shi},
journal= {arXiv preprint arXiv:2407.19312},
year = {2024}
}