Floquet Perturbation Theory: Formalism and Application to Low-Frequency Limit

TL;DR

This paper introduces a low-frequency perturbation theory within Floquet formalism for periodically driven quantum systems, unifying high- and low-frequency approaches and applying it to two-level and lattice fermion models.

Contribution

It develops a unified Floquet perturbation framework that captures adiabatic and diabatic effects, extending the applicability of Floquet theory to low-frequency regimes.

Findings

Reproduces known transition probabilities systematically

Clarifies the regime of applicability of Floquet approximations

Analyzes spectral properties and dynamics of driven lattice fermions

Abstract

We develop a low-frequency perturbation theory in the extended Floquet Hilbert space of a periodically driven quantum systems, which puts the high- and low-frequency approximations to the Floquet theory on the same footing. It captures adiabatic perturbation theories recently discussed in the literature as well as diabatic deviation due to Floquet resonances. For illustration, we apply our Floquet perturbation theory to a driven two-level system as in the Schwinger-Rabi and the Landau-Zener-St\"uckelberg-Majorana models. We reproduce some known expressions for transition probabilities in a simple and systematic way and clarify and extend their regime of applicability. We then apply the theory to a periodically-driven system of fermions on the lattice and obtain the spectral properties and the low-frequency dynamics of the system.