Quantum tunneling and its absence in deep wells and strong magnetic fields

• URL: http://arxiv.org/abs/2412.21100v2
• Date: Tue, 31 Dec 2024 05:55:21 GMT
• Title: Quantum tunneling and its absence in deep wells and strong magnetic fields
• Authors: Charles L. Fefferman, Jacob Shapiro, Michael I. Weinstein,
• Abstract summary: We construct a family of double well potentials containing examples for which the low-energy eigenvalue splitting vanishes. By deforming within this family, the magnetic ground state can be made to transition from symmetric to anti-symmetric.
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• Abstract: We present new results on quantum tunneling between deep potential wells, in the presence of a strong constant magnetic field. We construct a family of double well potentials containing examples for which the low-energy eigenvalue splitting vanishes, and hence quantum tunneling is eliminated. Further, by deforming within this family, the magnetic ground state can be made to transition from symmetric to anti-symmetric. However, for typical double wells in a certain regime, tunneling is not suppressed, and we provide a lower bound for the eigenvalue splitting.

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