2012/12/31 by Fabio L. Traversa, Massimiliano Di Ventra, Fabrizio Bonani · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Force Microscopy Techniques and Applications #Mechanical and Optical Resonators #Nonlinear Dynamics and Pattern Formation #math-ph #math.DS #math.MP #nlin.CD
paper · pdf · doi:10.1103/physrevlett.110.170602
published as Physical Review Letters, vol. 110, p. 170602, 2013
openalex publication_date 2013/04/24 · arxiv created 2013/05/01 · arxiv updated 2013/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Floquet theory is a powerful tool in the analysis of many physical phenomena, and extended to spatial coordinates provides the basis for Bloch's theorem. However, in its original formulation it is limited to linear systems with periodic coefficients. Here, we extend the theory by proving a theorem for the general class of systems including linear operators commuting with the period-shift operator. The present theorem greatly expands the range of applicability of Floquet theory to a multitude of phenomena that were previously inaccessible with this type of analysis, such as dynamical systems with memory. As an important extension, we also prove Bloch's theorem for nonlocal potentials.