Aperiodically driven integrable systems and their emergent steady states

For periodically driven closed quantum many-body systems, it is known
that the local properties of the system eventually synchronize with the
drive and can be described by an appropriate periodic Gibbs ensemble.
We have studied what happens in a class of integrable systems if they are
driven aperiodically. We show that the resulting unitary dynamics leads
to new emergent steady states in at least three cases. A random noise
causes eventual heating to an infinite temperature ensemble for all local
properties. A driving which is self-similar in time leads to an entirely different steady state which we call the `geometric generalized Gibbs ensemble'.
Finally, a quasiperiodic driving which follows the Fibonacci sequence can lead
to steady states which are not described by either a periodic Gibbs ensemble
or an infinite temperature ensemble. To understand the approach to the
steady state, we study the time evolution of certain coarse-grained
quantities in momentum space that fully determine the reduced density
matrices for subsystems whose sizes are much smaller than the full
system. Such quantities provide a concise description for any drive
protocol in integrable systems that are reducible to a free-fermion
representation.

References:

Nandy et al, Phys. Rev. X 7, 031034 (2017), and in preparation.