On global approximate controllability of a quantum particle in a box by moving walls
Optimization and Control
2024-03-05 v1 Mathematical Physics
math.MP
Quantum Physics
Abstract
We study a system composed of a free quantum particle trapped in a box whose walls can change their position. We prove the global approximate controllability of the system. That is, any initial state can be driven arbitrarily close to any target state in the Hilbert space of the free particle with a predetermined final position of the box. To this purpose we consider weak solutions of the Schr\"odinger equation and use a stability theorem for the time-dependent Schr\"odinger equation.
Keywords
Cite
@article{arxiv.2208.13475,
title = {On global approximate controllability of a quantum particle in a box by moving walls},
author = {Aitor Balmaseda and Davide Lonigro and Juan Manuel Pérez-Pardo},
journal= {arXiv preprint arXiv:2208.13475},
year = {2024}
}
Comments
25 pages, 1 figure