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arXiv · 2102.04425

Gauge invariance and Ward identities in nonlinear response theory

Habib Rostami·Mikhail I. Katsnelson·Giovanni Vignale·Marco Polini
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Abstract

We present a formal analysis of nonlinear response functions in terms of correlation functions in real- and imaginary-time domains. In particular, we show that causal nonlinear response functions, expressed in terms of nested commutators in real time, can be obtained from the analytic continuation of time-ordered response functions, which are more easily amenable to diagrammatic calculation. This generalizes the well-known result of linear response theory. We then use gauge invariance arguments to derive exact relations between second-order response functions in density and current channels. These identities, which are non-perturbative in the strength of inter-particle interactions, allow us to establish exact connections between nonlinear optics calculations done in different electromagnetic gauges.

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Habib Rostami, Mikhail I. Katsnelson, Giovanni Vignale, Marco Polini. 2021-02-08. Gauge invariance and Ward identities in nonlinear response theory. https://doi.org/10.1016/j.aop.2021.168523

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