Reducibility of the quantum harmonic oscillator in d-dimensions with finitely differentiable perturbations

2019/09/12 by Wenwen Jian, Jian, Wenwen
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Quantum Mechanics and Non-Hermitian Physics #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1909.05562

Abstract

In this paper, the d-dimensional quantum harmonic oscillator with a pseudo-differential time quasi-periodic perturbation iψ=(-Δ+V(x)+εW(ωt,x,-i∇))ψ, x∈ℝ^d is considered, where ω∈(0,2π)ⁿ, V(x):=∑_j=1^d v_j²x_j², v_j≥ v₀>0, and W(θ,x,ξ) is a real polynomial in (x,ξ) of degree at most two, with coefficients belonging to C^ℓ in θ∈\mathbbTⁿ for the order ℓ satisfying ℓ≥ 2n-1+β, 0

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