  Driven many-body quantum systems where some parameter in the Hamiltonian is
varied quasiperiodically in time may exhibit nonequilibrium steady states that
are qualitatively different from their periodically driven counterparts. Here
we consider a prototypical integrable spin system, the spin-$1/2$ transverse
field Ising model in one dimension, in a pulsed magnetic field. The time
dependence of the field is taken to be quasiperiodic by choosing the pulses to
be of two types that alternate according to a Fibonacci sequence. We show that
a novel steady state emerges after an exponentially long time when local
properties (or equivalently, reduced density matrices of subsystems with size
much smaller than the full system) are considered. We use the temporal
evolution of certain coarse-grained quantities in momentum space to understand
this nonequilibrium steady state in more detail and show that unlike the
previously known cases, this steady state is neither described by a periodic
generalized Gibbs ensemble nor by an infinite temperature ensemble. Finally, we
study a toy problem with a single two-level system driven by a Fibonacci
sequence; this problem shows how sensitive the nature of the final steady state
is to the different parameters.
