We developed a novel perturbative expansion for the effective Hamiltonian governing the dynamics of periodically kicked systems in the small parameter of the kick strength. The expansion is based on the replica trick, and is formally equivalent to the infinite resummation of the Baker-Campbell-Hausdorff series in the non-kicked Hamiltonian, while taking finite order terms in the kicks. As an application of the replica expansion, we study the heating properties of a periodically kicked spin chain. We demonstrate that even away from the high frequency driving limit, the heating rate is at least stretched exponentially suppressed in the kick strength. This leads to a long pre-thermal regime, where the dynamics is governed by the effective Hamiltonian obtained from the expansion.

* Szabolcs Vajna, Faculty of Mathematics and Physics, University of Ljubljana