#### Vol. 11, No. 3, 2018

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Reducibility of the quantum harmonic oscillator in $d$-dimensions with polynomial time-dependent perturbation

### Dario Bambusi, Benoît Grébert, Alberto Maspero and Didier Robert

Vol. 11 (2018), No. 3, 775–799
##### Abstract

We prove a reducibility result for a quantum harmonic oscillator in arbitrary dimension with arbitrary frequencies perturbed by a linear operator which is a polynomial of degree 2 in $\left({x}_{j},-i{\partial }_{j}\right)$ with coefficients which depend quasiperiodically on time.

##### Keywords
reducibility, harmonic oscillators, growth of Sobolev norms
##### Mathematical Subject Classification 2010
Primary: 35J10, 37K55
##### Milestones
Revised: 6 September 2017
Accepted: 16 October 2017
Published: 22 November 2017
##### Authors
 Dario Bambusi Dipartimento di Matematica Università degli Studi di Milano Milano Italy Benoît Grébert Laboratoire de Mathématiques Jean Leray Université de Nantes Nantes France Alberto Maspero International School for Advanced Studies (SISSA) Trieste Italy Didier Robert Laboratoire de Mathématiques Jean Leray Université de Nantes Nantes France