Towards a Unified Approach to Electromagnetic Fields and Quantum Currents From Dirac Spinors

Modeling the combined electromagnetic (EM)/quantum transport problem in graphene circuits requires the development of novel concepts and novel unified tools. In this paper, we further explore the correlation between Dirac and Maxwell equations, in the time domain, where we derive the transmission-line equations, valid for both EM and quantum current. This is a step forward toward an effective integration of the Dirac theory in the numerical simulation of EM field problems and introducing EM concepts and simulators to describe quantum transport. We show that the familiar Telegrapher's equations can be readapted in order to investigate the mechanisms that govern the space-time evolution of Dirac spinors; two significant examples, having a double quantum/EM meaning, are provided. Final considerations about associated quantum current have also been reported.