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We study chiral models in one spatial dimension, both static and periodicallydriven. We demonstrate that their topological properties may be read outthrough the long time limit of a bulk observable, the mean chiral displacement.The derivation of this result is done in terms of spectral projectors, allowingfor a detailed understanding of the physics. We show that the proposeddetection converges rapidly and it can be implemented in a wide class of chiralsystems. Furthermore, it can measure arbitrary winding numbers and topologicalboundaries, it applies to all non-interacting systems, independently of theirquantum statistics, and it requires no additional elements, such as externalfields, nor filled bands.

Topological characterization of chiral models through their long time dynamics