Reducibility of the Quantum Harmonic Oscillator in d-dimensions with Polynomial Time Dependent Perturbation

Dario Bambusi (1) , Benoît Grébert (2) , Alberto Maspero (2) , Didier Robert (2)

1 Dipartimento de Matematica [Milano]
2 LMJL - Laboratoire de Mathématiques Jean Leray

We prove a reducibility result for a quantum harmonic oscillator in arbitrary dimensions with arbitrary frequencies perturbed by a linear operator which is a polynomial of degree two in $x_j$, $-i \partial_j$ with coefficients which depend quasiperiodically on time.

Domaines: Physique mathématique [math-ph]

Dario Bambusi, Benoît Grébert, Alberto Maspero, Didier Robert. Reducibility of the Quantum Harmonic Oscillator in d-dimensions with Polynomial Time Dependent Perturbation. 2017. ⟨hal-01471363⟩