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We study the isotropic XY chain with a transverse magnetic field acting on asingle site and analyse the long time behaviour of the time-dependent state ofthe system when a periodic perturbation drives the impurity. We find that forhigh frequencies the state approaches a periodic orbit synchronised with theforcing and provide the explicit rate of convergence to the asymptotics.

Periodic Driving at High Frequencies of an Impurity in the Isotropic XY Chain