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A comparative study of perturbative and nonequilibrium Green's function approaches for Floquet sidebands in periodically driven quantum systems

Karun Gadge, Marco Merboldt, Michael Schüler, Jan Philipp Bange, Wiebke Bennecke, Michael A. Sentef, Marcel Reutzel, Stefan Mathias, Salvatore R. Manmana

Published Jan 20, 2026• 1 citation
Publisher

Abstract

This repository only contains the data that shown in the manuscript. See README file for the structure. Same as V1, with complete list of authors.
DOI
10.5281/zenodo.18315670

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This data repository contains the information necessary to reproduce the main results of the paper “A quantum annealer with fully programmable all-to-all coupling via Floquet engineering”. The repository contains both the data required to generate each of the figures of the main manuscript, as well as source code for running simulations of the proposed scheme. Please note that the project was conducted in Julia version 0.6, which can be downloaded from https://julialang.org/downloads/oldreleases/. The repository is structured around each of the figures of the main manuscript. Please read the README for a summary of the structure of each folder, as well as the guidelines for generating the corresponding figure and running the corresponding source code.
We derive an analytical expression for the steady-state quantum statistics of periodically driven quantum systems coupled to a bath using the nonequilibrium Green's function (NEGF) formalism. By embedding Floquet theory into NEGF, we obtain closed expressions for the retarded, advanced, and lesser Green's functions in the Floquet representation, yielding the Floquet Fermi distribution in which the steady-state occupation is expressed as a weighted sum of Fermi functions shifted by integer multiples of the driving frequency. The weights are determined solely by the Fourier components of the micromotion operator, providing a transparent interpretation of Floquet sideband occupations. Our analysis extends beyond the diagonal commuting Hamiltonians treated in earlier work, and further shows that the robust Floquet distribution remains valid for a broad class of weakly coupled bath spectral functions beyond the ideal featureless-bath approximation. Finally, we establish a Floquet version of the Landauer formula for the DC part of the current, in which the equilibrium Fermi functions are replaced by their Floquet-modified counterparts. Together, these results provide a coherent description of Floquet quantum statistics and transport in periodically driven open quantum systems.
This repository contains datasets and Python scripts used to generate the numerical results related to [M. Tokieda, Work-minimizing protocols in driven-dissipative quantum systems: An impulse-ansatz approach, arXiv:2511.15084 [quant-ph]]. Parts of the manuscript and computational procedures have been revised. An updated version of the manuscript is available as manuscript.pdf in this repository. Note: Unicode characters (e.g., τ, β) in filenames may not render correctly in Zenodo’s web preview. The downloaded archive should be unaffected. If you experience any issues accessing or extracting the files, please do not hesitate to contact the author.