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Are there any ab initio packages that take advantage of Floquet's theorem (which one can think of as a generalization of Bloch's theorem from space to time) in order to study the impact of an oscillating electric field on the electronic energies of the system?

Or, would one study such systems with a different ab initio approach?

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Emilio Artacho's group has used Floquet theory to look at the behavior of projectiles in crystalline solids. You can read about it here (open access): Floquet theory for the electronic stopping of projectiles in solids.

Perhaps not exactly what you asked for, but it is an example of Floquet theory applied to electrons in condensed matter.

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