Field patterns: A new type of wave with infinitely degenerate band structure

• Published in: Europhysics letters Vol. 120; no. 5; pp. 54003 - 54008
• Main Authors: Mattei, Ornella, Milton, Graeme W.
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences, IOP Publishing and Società Italiana di Fisica 01.12.2017; IOP Publishing
• Subjects: 42.25.Bs; 77.84.Lf; 81.05.Zx; Chaos theory; Dimensional changes; Disturbances; Relativity; Spacetime; Spatial distribution
• ISSN: 0295-5075; 1286-4854
• DOI: 10.1209/0295-5075/120/54003

Field pattern materials (FP-materials) are space-time composites with PT-symmetry in which the one-dimensional-spatial distribution of the constituents changes in time in such a special manner to give rise to a new type of waves, which we call field pattern waves (FP-waves) (Milton G. W. and Mattei O., Proc. R. Soc. A, 473 (2017) 20160819; Mattei O. and Milton G. W., New J. Phys., 19 (2017) 093022). Specifically, due to the special periodic space-time geometry of these materials, when an instantaneous disturbance propagates through the system, the branching of the characteristic lines at the space-time interfaces between phases does not lead to a chaotic cascade of disturbances but concentrates on an orderly pattern of disturbances: this is the field pattern. In this letter, by applying Bloch-Floquet theory, we show that the dispersion diagrams associated with these FP-materials are infinitely degenerate: associated with each point on the dispersion diagram is an infinite space of Bloch functions. Each generalized function is concentrated on a specific field pattern, each parameterized by a variable that we call the launch parameter. The dynamics separates into independent dynamics on the different field patterns, each with the same dispersion relation.