Quantum kinetics of refocusing

We consider quantum kinetics of an open quantum system in the presence of periodic fields designed to suppress the internal evolution and shield the system from generic low-frequency environment (refocusing or dynamical decoupling in application to multi-qubit systems). Assuming that the refocusing has order K, that is, for frozen environment the cumulant expansion of the evolution operator over the period tau begins with the term ~tau^(K+1), we trace the associated cancellations in the kernel of the quantum kinetic equation in the Floquet formalism and characterize the remaining decoherence processes.