Tunneling estimates for two-dimensional perturbed magnetic Dirac systems

Abstract

We prove tunneling estimates for two-dimensional Dirac systems which are localized in space due to the presence of a magnetic field. The Hamiltonian driving the motion admits the decomposition $H=H_0+W$, where $H_0$ is a rotationally symmetric magnetic Dirac operator and $W$ is a position-dependent matrix-valued potential satisfying certain smoothness condition in the angular variable. A consequence of our results are upper bounds for the growth in time of the expected size of the system and its total angular momentum.

Dedicated to the memory of Georgi Raikov