Tunneling Estimates for Two-Dimensional Perturbed Magnetic Dirac Systems

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 \( H = H_0 + W\) $H=H_0+W$ , where \(H_0 \) $H_0$ 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.