An example of a small-time globally approximately controllable bilinear Schr\" odinger equation

K Beauchard, E Pozzoli - arXiv preprint arXiv:2407.05698, 2024 - arxiv.org
A variety of physically relevant bilinear Schr\" odinger equations are known to be globally
approximately controllable in large times. There are however examples which are globally …

Small-time local controllability of the bilinear Schr\" odinger equation, despite a quadratic obstruction, thanks to a cubic term

M Bournissou - arXiv preprint arXiv:2203.03955, 2022 - arxiv.org
We consider a 1D linear Schr {\" o} dinger equation, on a bounded interval, with Dirichlet
boundary conditions and bilinear control. We study its controllability around the ground state …

Simultaneous global exact controllability in projection of infinite 1D bilinear Schr\" odinger equations

A Duca - arXiv preprint arXiv:1703.00966, 2017 - arxiv.org
The aim of this work is to study the controllability of infinite bilinear Schr\" odinger equations
on a segment. We consider the equations (BSE) $ i\partial_t\psi^{j}=-\Delta\psi^ j+ u (t) B\psi …

Controllability of bilinear quantum systems in explicit times via explicit control fields

A Duca - International Journal of Control, 2021 - Taylor & Francis
Full article: Controllability of bilinear quantum systems in explicit times via explicit control fields
Skip to Main Content Taylor and Francis Online homepage Taylor and Francis Online …

Local controllability of the bilinear 1D Schr {\" o} dinger equation with simultaneous estimates

M Bournissou - arXiv preprint arXiv:2107.08817, 2021 - arxiv.org
We consider the 1D linear Schr {\" o} dinger equation, on a bounded interval, with Dirichlet
boundary conditions and bilinear scalar control. The small-time local exact controllability …

Quadratic behaviors of the 1D linear Schrödinger equation with bilinear control

M Bournissou - Journal of Differential Equations, 2023 - Elsevier
We consider a 1D linear Schrödinger equation, on a bounded interval, with Dirichlet
boundary conditions and bilinear control. We study its controllability around the ground state …

Small-time controllability on the group of diffeomorphisms for Schr\" odinger equations

K Beauchard, E Pozzoli - arXiv preprint arXiv:2410.02383, 2024 - arxiv.org
In this work, we establish a link between the small-time approximate controllability of bilinear
Schr\" odinger PDEs (posed on a boundaryless Riemannian manifold $ M $) and the control …

Quantum control in infinite dimensions and Banach-Lie algebras: Pure point spectrum

M Keyl - arXiv preprint arXiv:1812.09211, 2018 - arxiv.org
In finite dimensions, controllability of bilinear quantum control systems can be decided quite
easily in terms of the" Lie algebra rank condition"(LARC), such that only the systems Lie …

[PDF][PDF] Simultaneous global exact controllability in projection

A Duca - submitted: https://arxiv. org/abs/1703.00966, 2018 - hal.science
Simultaneous global exact controllability in projection Page 1 Simultaneous global exact
controllability in projection Alessandro Duca Laboratoire de Mathématiques de Besançon …

Controlling a d-level atom in a cavity

T Hofmann, M Keyl - arXiv preprint arXiv:1712.07613, 2017 - arxiv.org
In this paper we study controllability of a $ d $-level atom interacting with the
electromagnetic field in a cavity. The system is modelled by an ordered graph $\Gamma …