Electric field effects on motion of a charged particle through a saddle potential in a magnetic field

The role of an electric field in electron transmission through a quantum point contact (QPC) in the presence of a magnetic field is analyzed here, modeling the QPC as a saddle potential. In this paper, we derive the relevant Green's function, including the effects of arbitrarily time-dependent electric and constant magnetic fields. The derivation is carried out using Schwinger's operator equation of motion approach. In the second part of the paper, we apply the Green's function to determine transmission of the electron guiding center through the QPC in constant electric and magnetic fields.