Current-conserving nonlinear response theory in driven systems

TL;DR

This paper develops a current-conserving nonlinear response theory for driven electronic systems using the closed-time path 2PI effective action, ensuring gauge invariance and current conservation beyond mean-field approximations.

Contribution

It introduces a systematic approach to calculate response functions that inherently satisfy current conservation through gauge invariance of the 2PI effective action.

Findings

Response functions obey Ward-Takahashi identities

Current conservation is maintained beyond mean-field level

Framework applicable to electronic pumping devices

Abstract

Employing the closed-time path 2PI effective action (CTP 2PI EA) approach, we study the response of an open interacting electronic system to time-dependent external electromagnetic fields. We show that the 2PI EA provides a systematic way of calculating the propagator and response functions of the system. Due to the invariance of the 2PI EA under external gauge transformations, the response functions calculated from it are such that the Ward-Takahashi hierarchy, that ensures current conservation beyond the expectation value level, is satisfied. These findings may be useful in the study of interacting electronic pumping devices, and serve to clarify the connection between current conservation (beyond the mean value level) and real-time nonlinear response theory.