Thouless adiabatic quantum pumping  is a cornerstone in condensed matter physics. It lays the conceptual foundations to many aspects of the field of topological insulators. Recently, systems explictly realizing a topological quantum pump have been realized in cold-atom experiments. In this work, we study what happens out of the perfect adiabatic limit. Within a Floquet framework, we analyze the features of the transported charge as a function of the frequency of the driving. Most importantly, we find that the system is not topologically robust to non-adiabatic effects. The long-time average value of the trasported charge, described by the Floquet diagonal ensemble, shows deviations from the topologically quantized limit which are quadratic in the frequency, on the contrary of previous works , which found instead exponentially small corrections to the quantized value. The charge transported in the first period shows beatings-like oscillations on top of the diagonal value, in accordance with a theorem of Avron and Kons .
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