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arXiv · 2609.21078

Double-wells in a strong magnetic field: absence of tunneling for infinitely many values of the coupling constant

Kevin Buck·Charles L. Fefferman·Javier Gómez-Serrano·Amaury Hayat·Jacob Shapiro·Michael I. Weinstein
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Abstract

We prove the fixed-potential conjecture of Fefferman, Shapiro, and Weinstein for inversion-symmetric magnetic double wells. We construct a number $L_0>0$ and one smooth, compactly supported, nonpositive, nonradial single-well potential $v$, independent of both the coupling parameter $λ$ and the well displacement, such that for every fixed $L\ge L_0$ the associated magnetic double-well Hamiltonian has infinitely many exact degeneracies of its two lowest eigenvalues as $λ\to\infty$. The magnetic hopping coefficient also vanishes along an infinite sequence tending to infinity. The potential consists of a radial core and two small, reflection-related perturbations supported on one-sided quadratic cusps. Their log-flat profiles isolate two dominant hopping contributions, which we evaluate by steepest descent after inserting the radial ground-state asymptotics. The resulting asymptotic cosine expression, together with error bounds for the even--odd splitting, yields infinitely many exact eigenvalue crossings and changes of ground-state parity.

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Kevin Buck, Charles L. Fefferman, Javier Gómez-Serrano, Amaury Hayat, Jacob Shapiro, Michael I. Weinstein. 2026-09-17. Double-wells in a strong magnetic field: absence of tunneling for infinitely many values of the coupling constant. https://arxiv.org/abs/2609.21078

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