Average lower bound on magnetic double-well tunneling with asymptotically large well separation
Abstract
We study tunneling between two identical, smooth, compactly supported potential wells in a constant perpendicular magnetic field, with the coupling and magnetic field fixed and the well separation tending to infinity. For a sufficiently small positive magnetic field, we prove lower bounds on the hopping coefficient and on the splitting of the two lowest eigenvalues outside a set of separations of density zero. If the well centers are separated by 2d1 and the magnetic field strength is bλ, the lower bounds have the form e−bλd12−Cd11+δ for every fixed δ∈(0,1). No radial or reflection symmetry of the single-well potential is assumed. The proof combines the explicit Landau resolvent kernel with a complex analytic estimate for logarithmic averages of the hopping coefficient.
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BibTeX
@misc{fefferman2026average,
title = {{Average lower bound on magnetic double-well tunneling with asymptotically large well separation}},
author = {Charles L. Fefferman and Say-Yeon Kwon and Jacob Shapiro and Michael I. Weinstein},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26637},
eprint = {2610.26637},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26637},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Average lower bound on magnetic double-well tunneling with asymptotically large well separation
AU - Charles L. Fefferman
AU - Say-Yeon Kwon
AU - Jacob Shapiro
AU - Michael I. Weinstein
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26637
UR - https://arxiv.org/abs/2610.26637
AB - We study tunneling between two identical, smooth, compactly supported potential wells in a constant perpendicular magnetic field, with the coupling and magnetic field fixed and the well separation tending to infinity. For a sufficiently small positive magnetic field, we prove lower bounds on the hopping coefficient and on the splitting of the two lowest eigenvalues outside a set of separations of density zero. If the well centers are separated by 2d_1 and the magnetic field strength is bλ, the lower bounds have the form e^−bλd_1^2−Cd_1^1+δ for every fixed δ∈(0,1). No radial or reflection symmetry of the single-well potential is assumed. The proof combines the explicit Landau resolvent kernel with a complex analytic estimate for logarithmic averages of the hopping coefficient.
ER -