nLab Floquet theory

Idea

In solid state physics, Floquet theory is concerned with quantum systems which are driven by time-periodic external forces/potentials. The archetypical case is the study of electrons in a crystal subjected to a strong and periodically oscillating electromagnetic field.

This way, Floquet theory may be understood as the temporal analog of what for spatial periodicity is the subject of Bloch theory.

References

Textbook account:

• Thomas Dittrich, Peter Hänggi, Gert-Ludwig Ingold, Bernhard Kramer, Gerd Schön, W. Zwerger; Chapter 5 in: Quantum Transport and Dissipation, Wiley-VCH (1998) [pdf]

Lecture notes:

• Giuseppe E. Santoro: Introduction to Floquet, lecture at SFT 2019 – Lectures on Statstical Field Theory (2019) [pdf]

• Konrad Viebahn: Introduction to Floquet theory (2020) [pdf]

See also:

• Wikipedia: Floquet theory

• Grokipedia: Floquet theory

For open quantum systems:

• Masahiro Sato, Tatsuhiko N. Ikeda: Floquet theory and applications in open quantum and classical systems, J. Phys. Soc. Jpn. 94 111007 (2025) [arXiv:2508.01783, doi:10.7566/JPSJ.94.111007]