KAM for high-dimensional nonlinear quantum harmonic oscillator

Fuente: arXiv
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Main Authors: Liu, Jianjun, Qi, Caihong, Shi, Guanghua
Format: Preprint
Published: 2024
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_version_ 1866909270655631360
author Liu, Jianjun
Qi, Caihong
Shi, Guanghua
author_facet Liu, Jianjun
Qi, Caihong
Shi, Guanghua
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_19312
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle KAM for high-dimensional nonlinear quantum harmonic oscillator
Liu, Jianjun
Qi, Caihong
Shi, Guanghua
Analysis of PDEs
Dynamical Systems
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.
title KAM for high-dimensional nonlinear quantum harmonic oscillator
topic Analysis of PDEs
Dynamical Systems
url https://arxiv.org/abs/2407.19312