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arXiv · 2407.19312

KAM for high-dimensional nonlinear quantum harmonic oscillator

Jianjun Liu·Caihong Qi·Guanghua Shi
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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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Jianjun Liu, Caihong Qi, Guanghua Shi. 2024-07-27. KAM for high-dimensional nonlinear quantum harmonic oscillator. https://arxiv.org/abs/2407.19312

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