dorsal/arxiv
View SchemaSmooth Controllability of Infinite Dimensional Quantum Mechanical Systems
| Authors | Re-Bing Wu, Tzyh-Jong Tarn, Chun-Wen Li |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0505063 |
| URL | https://arxiv.org/abs/quant-ph/0505063 |
| DOI | 10.1103/PhysRevA.73.012719 |
Abstract
Manipulation of infinite dimensional quantum systems is important to controlling complex quantum dynamics with many practical physical and chemical backgrounds. In this paper, a general investigation is casted to the controllability problem of quantum systems evolving on infinite dimensional manifolds. Recognizing that such problems are related with infinite dimensional controllability algebras, we introduce an algebraic mathematical framework to describe quantum control systems possessing such controllability algebras. Then we present the concept of smooth controllability on infinite dimensional manifolds, and draw the main result on approximate strong smooth controllability. This is a nontrivial extension of the existing controllability results based on the analysis over finite dimensional vector spaces to analysis over infinite dimensional manifolds. It also opens up many interesting problems for future studies.
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"date_created": "2026-03-02T18:02:16.810000Z",
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"abstract": "Manipulation of infinite dimensional quantum systems is important to\ncontrolling complex quantum dynamics with many practical physical and chemical\nbackgrounds. In this paper, a general investigation is casted to the\ncontrollability problem of quantum systems evolving on infinite dimensional\nmanifolds. Recognizing that such problems are related with infinite dimensional\ncontrollability algebras, we introduce an algebraic mathematical framework to\ndescribe quantum control systems possessing such controllability algebras. Then\nwe present the concept of smooth controllability on infinite dimensional\nmanifolds, and draw the main result on approximate strong smooth\ncontrollability. This is a nontrivial extension of the existing controllability\nresults based on the analysis over finite dimensional vector spaces to analysis\nover infinite dimensional manifolds. It also opens up many interesting problems\nfor future studies.",
"arxiv_id": "quant-ph/0505063",
"authors": [
"Re-Bing Wu",
"Tzyh-Jong Tarn",
"Chun-Wen Li"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.012719",
"title": "Smooth Controllability of Infinite Dimensional Quantum Mechanical Systems",
"url": "https://arxiv.org/abs/quant-ph/0505063"
},
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