Aperiodically and quasi-periodically driven closed integrable quantum systems
ABSTRACT :
The study of periodically driven closed quantum systems is an exciting as well as a challenging area of recent research that has come to the fore, both from experimental and theoretical perspectives. Whether a closed integrable system heats up indefinitely or reaches a steady is a very relevant question in this regard. For a periodically driven closed integrable systems, it is usually believed that the system reaches a periodic steady state in the asymptotic limit of driving and hence stops absorbing energy. What we shall discuss below even in this most favorable case, slightest deviation from the perfect periodicity, which is experimentally inevitable, would always result in heating up of the system indefinitely. On the other hand, when the system is driven by two (non-commuting) Hamiltonians chosen from a Fibonacci sequence, in the high frequency limit of driving, for each momenta $k$, the periodically observed state lies between two concentric circles and the system reaches a non-equilibrium steady state. In this talk, I shall discuss these situations starting from the simplest situation.