Under a non-resonance frequency condition and weak coupling, the asymptotic state of a locally driven isotropic XY chain is a periodic solution of the Floquet-Schrodinger equation, with convergence rate O(1/sqrt(t-t0)).
Genovese, On the Dynamics of XY Spin Chains with Impurities , Physica A, 434, 36, (2015)
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Long time behaviour of a local perturbation in the isotropic XY chain under periodic forcing
Under a non-resonance frequency condition and weak coupling, the asymptotic state of a locally driven isotropic XY chain is a periodic solution of the Floquet-Schrodinger equation, with convergence rate O(1/sqrt(t-t0)).