Time Quasicrystals in Dissipative Dynamical Systems
Mathematical Physics Seminar
29th September 2017, 2:00 pm – 3:00 pm
Howard House, 4th Floor Seminar Room
Quasicrystals are aperiodic tilings of space, lying between periodicity and disorder, which can be constructed as slices through higher-dimensional crystals. In this talk we ask whether quasicrystalline order can be generalized to the time direction. Such a`time quasicrystal' would be composed of bars of two different durations appearing in a non-repeating pattern. Nevertheless, the sequence would be long-range ordered, as seen by viewing the structure in a space spanned by two perpendicular directions of time. We identify these structures as stable trajectories in the chaotic regime of certain nonlinear dynamical systems. We find that, of the ten physically-relevant 1D quasicrystals, precisely two can form time quasicrystals. We term these the infinite Pell and Clapeyron words, and show that they grow through a generalization of the period-doubling cascade into chaos. Successive tiers of the cascade constitute systematically-improved periodic approximations which allow a physical implementation of the results.