Year: 2025
Type: preprint
Abstract: The two-dimensional magnetic Laplacian is considered. We calculate the leading term of the splitting between the first two eigenvalues of the operator in the semiclassical limit under the assumption that the magnetic field does not vanish and has two symmetric magnetic wells with respect to the coordinate axes. This is the first result of quantum tunneling between purely magnetic wells under generic assumptions. The proof, which strongly relies on microlocal analysis, reveals a purely magnetic Agmon distance between the wells. Surprisingly, it is discovered that the exponential decay of the eigenfunctions away from the magnetic wells is not crucial to derive the tunneling formula. The key is a microlocal exponential decay inside the characteristic manifold, with respect to the variable quantizing the classical center guide motion.
Source: arXiv (Cornell University)
Authors: Fournais, Søren, Bonthonneau, Yannick Guedes, Morin, Léo, Raymond, Nicolas
Institutions: University of Copenhagen, Centre National de la Recherche Scientifique, Université Sorbonne Paris Nord, Laboratoire Analyse, Géométrie et Applications, Institut National des Sciences Mathématiques et de leurs Interactions, Laboratoire Angevin de Recherche en Mathématiques, Université d'Angers
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414849657