Average lower bound on magnetic double-well tunneling with asymptotically large well separation
Year: 2026
Type: preprint
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 $2d_1$ and the magnetic field strength is $bλ$, the lower bounds have the form $e^{-bλd_1^2-Cd_1^{1+δ}}$ for every fixed $δ\in(0,1)$. 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.
Source: arXiv (Cornell University)
Institutions: Princeton University, University of Vienna, Columbia University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223015741