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arXiv:2509.02857

Magnetic Double-Wells: Absence of Tunneling

Charles Fefferman, Jacob Shapiro, Michael I. Weinstein

Published Sep 2, 2025• 0 citations
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Abstract

We present a magnetic double-well Hamiltonian where the tunneling between the two wells vanishes, as recently announced.
DOI
10.48550/arxiv.2509.02857

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We present 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 antisymmetric. However, for typical double wells in a certain regime, tunneling is not suppressed, and we provide a lower bound for the eigenvalue splitting.
Inspired by a recent paper∗^*∗ by C. Fefferman, J. Shapiro and M. Weinstein, we investigate quantum tunneling for a Hamiltonian with a symmetric double well and a uniform magnetic field. In the simultaneous limit of strong magnetic field and deep potential wells with disjoint supports, tunneling occurs and we derive accurate estimates of its magnitude. ∗ ^*\,∗[Lower bound on quantum tunneling for strong magnetic fields. SIAM J. Math. Anal. 54(1), 1105-1130 (2022).]
In a previous work [H. Pu, W. Zhang, and P. Meystre, Phys. Rev. Lett. 87, 140405 (2001)]], we have shown that a spinor condensate confined in a periodic or double-well potential exhibits ferromagnetic behavior due to the magnetic dipole-dipole interactions between different wells, and in the absence of external magnetic field, the ground state has a twofold degeneracy. In this work, we demonstrate the possibility of observing macroscopic quantum spin tunneling between these two degenerate states and show how the tunneling rate critically depends on the strength of the transverse field.