Tunneling estimates for magnetic Schrödinger operators
The author studies the semiclassical exponential decay of the eigenfunctions of a bidimensional magnetic Schrödinger operator. The magnetic field \(B\) is assumed to be constant, and the electric potential \(V\) is supposed to form a simple well, and to be analytic with respect to rotations. Then, by conjugating the operator with a convenient exponential weight, the author finds a lower bound for the rate of decay of the eigenfunctions, which involves explicitly \(B\). In particular, this bound increases with \(| B|\), and it becomes optimal when \(V\) is assumed to be radial. An application to tunneling is also given when \(V\) is a smooth symmetric double well.
scientific article; zbMATH DE number 1271627