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Generalized Floquet theory: application to dynamical systems with memory and Bloch's theorem for nonlocal potentials
Fabio L Traversa1, Massimiliano Di Ventra, Fabrizio Bonani
1Departament d'Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193-Bellaterra, Barcelona, Spain. fabiolorenzo.traversa@uab.es
Physical Review Letters
|May 18, 2013
Summary
We extended Floquet theory to analyze complex systems, including those with memory. This advancement also enables proving Bloch
Area of Science:
- Mathematical Physics
- Dynamical Systems
Background:
- Floquet theory analyzes physical phenomena with periodic coefficients.
- Its application is limited to linear systems.
Purpose of the Study:
- Extend Floquet theory to a broader class of systems.
- Prove Bloch's theorem for nonlocal potentials.
Main Methods:
- Developed a generalized Floquet theorem.
- Applied it to systems with linear operators commuting with the period-shift operator.
Main Results:
- The generalized theorem expands Floquet theory's applicability.
- Demonstrated applicability to dynamical systems with memory.
- Proved Bloch's theorem for nonlocal potentials.
Conclusions:
- The extended Floquet theory offers a powerful new analytical tool.
- Opens new avenues for studying complex physical phenomena.
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