Gauge transformation for pulse propagation and time ordered integrals

TL;DR

This paper introduces a gauge transformation that simplifies pulse propagation analysis in quantum systems by renormalizing hoppings and reducing complex time-ordered integrals, aiding in the simulation of time-dependent quantum dynamics.

Contribution

It presents a novel gauge transformation method that simplifies the calculation of time evolution in quantum systems with time-dependent potentials.

Findings

Renormalizes inward and outward hoppings with phase factors

Facilitates reduction and simulation of pulse propagation

Simplifies time-ordered integrals in time-dependent Schrödinger equation

Abstract

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.