Effects of time defects in modulated systems (Vol. 51, No. 5)

The spatial periodicity in crystals induces energy band-gaps. Similarly, time modulated systems possess momentum band-gaps. Is there a temporal analogue to the localised edge modes induced by topological defects in spatial crystals?

We show that in a vertically vibrated liquid with a pi-shift in the excitation as a time defect, waves grow exponentially before the defect and decay exponentially after. Because of causality and non-energy conservation, this apparent time localisation must, in fact, be interpreted as a permutation of band-gap modes. However, as such, time defects provide an original way to explore these gaps.

G. d’Hardemare, A. Eddi and E. Fort, Probing Floquet modes in a time periodic system with time defects using Faraday instability, EPL 131, 24007 (2020)
[Abstract]