KAM for high-dimensional nonlinear quantum harmonic oscillator

2024/07/27 by Jian-Jun Liu, Liu, Jianjun, Caihong Qi +3
Physics and Astronomy · #Advanced Fiber Laser Technologies #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2407.19312

openalex publication_date 2024/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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