5 papers
An Example Of Accurate Microlocal Tunneling In One Dimension
Antide Duraffour, Nicolas Raymond
We investigate the spectral analysis of a class of pseudo-differential operators in one dimension. Under symmetry assumptions, we prove an asymptotic formula for the splitting of t…
The Laplacian with complex magnetic fields
David Krejcirik, Tho Nguyen Duc, Nicolas Raymond
We study the two-dimensional magnetic Laplacian when the magnetic field is allowed to be complex-valued. Under the assumption that the imaginary part of the magnetic potential is r…
Tunneling between magnetic wells in two dimensions
Søren Fournais, Yannick Guedes Bonthonneau, Léo Morin +1
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 un…
The superadiabatic projectors method applied to the spectral theory of magnetic operators
Lino Benedetto, Clotilde Fermanian Kammerer, Nicolas Raymond +1
This article deals with a generalization of the superadiabatic projectors method. In a general framework, the well-known superadiabatic projectors are constructed and accurately de…
Abrupt changes in the spectra of the Laplacian with constant complex magnetic field
David Krejcirik, Tho Nguyen Duc, Nicolas Raymond
We analyze the spectrum of the Laplace operator, subject to homogeneous complex magnetic fields in the plane. For real magnetic fields, it is well-known that the spectrum consists…