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 (xj,ij) with coefficients which depend quasiperiodically on time.

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Keywords
reducibility, harmonic oscillators, growth of Sobolev norms
Mathematical Subject Classification 2010
Primary: 35J10, 37K55
Milestones
Received: 18 February 2017
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