Magnetic tuning of quantum backflow: Schrödinger vs Pauli system

Abstract: Probability backflow is investigated for charged spin-$1/2$ particles in a uniform magnetic field within the lowest-Landau-level approximation. While single-mode Landau states exhibit only weak and non-robust backflow, it is shown that two-mode interference gives rise to negative probability flux in both the Schrödinger and Pauli formulations. In the Pauli case, orbital and spin contributions to the probability current are explicitly separated, revealing an additional interference mechanism. The external magnetic field is found to act as a tunable control parameter, simultaneously controlling the spatial overlap of orbitals and the spin dynamics. In the two-mode regime, a resonance between orbital mismatch and spin precession leads to an enhancement of backflow. Finite spatial resolution is shown not to suppress the effect within realistic coarse-graining. These results establish magnetic-field-controlled quantum backflow in Landau systems as an accessible interference phenomenon.