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KAM for high-dimensional nonlinear quantum harmonic oscillator (2407.19312v1)
Published 27 Jul 2024 in math.AP and math.DS
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.