Reducibility of Quantum Harmonic Oscillator on $\mathbb{R}^d$ Perturbed by a Quasi-periodic Potential with Logarithmic Decay

Abstract

We prove the reducibility of quantum harmonic oscillators in R d perturbed by a quasi-periodic in time potential V (x, ωt) with logarithmic decay. By a new estimate built for solving the homological equation we improve the reducibility result by Grébert-Paturel(Annales de la Faculté des sciences de Toulouse : Mathématiques. 28, 2019).