In the first part of my talk, I will discuss the equilibration of integrable systems in presence of aperiodic driving. We show that the presence of minimal randomness or aperiodicity on top of a perfectly periodic driving destabilizes the periodic steady-state, which is observed in the perfectly periodic situation. We demonstrate this result by incorporating a temporal binary randomness in an otherwise periodic driving. Within an exact analytical framework, we will show that the system, although integrable, reaches an infinite temperature ensemble in asymptotic time . We further study the nature of the asymptotic steady state in the case of a quasi-periodic (such as the Fibonacci sequence) driving protocol . In the second part of my talk, I will discuss the propagation of quantum correlations when an integrable system is coupled to a Markovian bath and explain the results within a quasi-particle picture, where the quasi-particles have a finite lifetime in contrast to isolated systems .
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