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Quantum tunneling in deep
potential wells and strong magnetic field revisited
Bernard Helffer and Ayman Kachmar |
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Vol. 6 (2024), No. 2, 319–352
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Abstract |
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We investigate a Hamiltonian with a symmetric double well and a uniform magnetic field, where tunneling occurs in the simultaneous limit of strong magnetic field and deep potential wells with disjoint supports. We derive an accurate estimate of its magnitude, and obtain a precise leading order asymptotic expression for the effect of a strong magnetic field, improving on the upper and lower bounds established earlier by Fefferman, Shapiro and Weinstein. |
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Keywords
Schrödinger operators, semiclassical techniques, WKB
methods, quantum tunneling, magnetic Laplacian
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Mathematical Subject Classification
Primary: 35P20, 81Q10, 81U26
Secondary: 82D20
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Milestones
Received: 6 January 2023
Revised: 22 November 2023
Accepted: 2 January 2024
Published: 16 May 2024
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Authors |
| Bernard Helffer | |
| Laboratoire de Mathématiques Jean
Leray, CNRS Nantes Université Nantes France |
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| Ayman Kachmar | |
| School of Science and
Engineering The Chinese University of Hong Kong (Shenzhen) Shenzhen China |
Department of Mathematics Lebanese University Nabatieh Lebanon |
| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
