Positivity of the spectral densities of retarded Floquet Green functions

TL;DR

This paper derives a spectral representation for retarded Floquet Green functions in periodically driven systems, proving spectral densities are nonnegative and establishing sum rules for benchmarking approximations.

Contribution

It generalizes the Lehmann representation to Floquet systems, enabling rigorous analysis of spectral properties in nonequilibrium quantum physics.

Findings

Spectral densities are proven to be nonnegative.

Exact spectral sum rules are established.

The representation aids in benchmarking approximations.

Abstract

Periodically driven nonequilibrium many-body systems are interesting because they have a quasi-energy spectra, which can be tailored by controlling the external driving fields. We derive the general spectral representation of retarded Green functions in the Floquet regime, thereby generalizing the well-known Lehmann representation from equilibrium many-body physics. The derived spectral Floquet representation allows us to prove the nonnegativity of spectral densities and to determine exact spectral sum rules, which can be employed to benchmark the accuracy of approximations to the exact Floquet many-body Green functions.