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arXiv 2108.00495math-phmath.MPmath.OCquant-ph
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通过磁势与边界条件实现类图流形上的量子可控性

Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions

Aitor Balmaseda, Davide Lonigro, Juan Manuel Pérez-Pardo

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 Schrödinger equation appear in arXiv:2306.10203. This new version is the one accepted for publication
发表信息：
J. Phys. A: Math. Theor. 56 (2023), 325201
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AI总结：

该研究针对厚量子图上的量子粒子这一无穷维系统，证明通过边界条件控制或含时磁场两种方案，均可实现全局近似可控性，为类图流形上的量子控制提供了理论依据。

摘要：

我们研究了一类无穷维量子系统的可控性：被限制在厚量子图（Thick Quantum Graph，量子图的推广，其边允许为任意维的流形且满足准δ边界条件）上的量子粒子。准δ边界条件是一类与图结构兼容的自伴边界条件。我们证明，通过两种物理上不同的方案可实现全局近似可控性：一是将边界条件作为控制量，二是使用含时磁场；两种情况的哈密顿量都具有含时定义域。

英文摘要：

We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with quasi-$δ$ boundary conditions. This is a particular class of self-adjoint boundary conditions compatible with the graph structure. We prove that global approximate controllability can be achieved using two physically distinct protocols: either using the boundary conditions as controls, or using time-dependent magnetic fields. Both cases have time-dependent domains for the Hamiltonians.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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