Gauge transformation for pulse propagation and time ordered integrals

We investigate a gauge transformation based on the successive elimination of time-dependent onsite potentials at individual sites in finite or infinite systems. Our analysis shows that this transformation renormalizes the inward hoppings by a phase factor $e^{i\phi (t)}$ and the outward hoppings by $e^{-i\phi (t)}$. We further demonstrate how this procedure facilitates the reduction and simulation of pulse propagation in scattering systems, while significantly simplifying the time-ordered integrals involved in the time evolution operator for time-dependent Schrodinger equation.