{"title":"Quantum Tunneling and the Aharonov-Bohm effect","authors":"Bernard Helffer, Ayman Kachmar","doi":"arxiv-2407.16524","DOIUrl":null,"url":null,"abstract":"We investigate a Hamiltonian with radial potential wells and an Aharonov-Bohm\nvector potential with two poles. Assuming that the potential wells are\nsymmetric, we derive the semi-classical asymptotics of the splitting between\nthe ground and second state energies. The flux effects due to the Aharonov-Bohm\nvector potential are of lower order compared to the contributions coming from\nthe potential wells.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"41 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Spectral Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.16524","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate a Hamiltonian with radial potential wells and an Aharonov-Bohm
vector potential with two poles. Assuming that the potential wells are
symmetric, we derive the semi-classical asymptotics of the splitting between
the ground and second state energies. The flux effects due to the Aharonov-Bohm
vector potential are of lower order compared to the contributions coming from
the potential wells.
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