通过磁势与边界条件在图状流形上的量子可控性
数学物理
2023-07-20 v4 math.MP
最优化与控制
量子物理
摘要
我们研究一个无限维量子系统的可控性：一个被限制在厚量子图（Thick Quantum Graph）上的量子粒子，厚量子图是量子图的一般化，其边允许为具有拟- 边界条件的任意维流形。这是一类与图结构相容的自伴边界条件。我们证明，使用两种物理上不同的协议可实现全局近似可控性：或将边界条件作为控制，或使用含时磁场。两种情形下哈密顿量均具有含时定义域。
引用
@article{arxiv.2108.00495,
title = {Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions},
author = {Aitor Balmaseda and Davide Lonigro and Juan Manuel Pérez-Pardo},
journal= {arXiv preprint arXiv:2108.00495},
year = {2023}
}
备注
The results on this article arise from splitting in two the original version. This contains the controllability results on higher dimensional versions of Quantum Graphs with magnetic laplacians. The results about existence and stability of the solutions of the non-autonomous Schr\"odinger equation appear in arXiv:2306.10203. This new version is the one accepted for publication