When an integrable system is driven periodically in time, it is known that the eventual steady state can be described by a generalized Gibbs ensemble. We will discuss what happens when an integrable system is driven aperiodically. In our calculations we will consider the one-dimensional Ising model in a transverse field which is driven in different ways. We will look at three kinds of aperiodic driving:
driving with a random noise, with a scale-invariant sequence (Thue-Morse) and with a quasiperiodic sequence (Fibonacci). We find that a random noise leads to the infinite temperature ensemble while the Thue-Morse sequence eventually (after an astronomically long time) leads to a periodic steady state because of some conserved quantities. The Fibonacci sequence leads to a wide variety of long-time behaviors, which are generally neither periodic nor infinite temperature states. However some limiting cases lead to almost periodic steady states.
References:
Nandy, Sen and Sen, Phys. Rev. X 7, 031034 (2017) and
Phys. Rev. B 98, 245144 (2018)
Maity, Bhattacharya, Dutta and Sen, Phys. Rev. B 99, 020306(R) (2019
