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arXiv · 1908.09035

Long time behaviour of a local perturbation in the isotropic XY chain under periodic forcing

Livia Corsi·Giuseppe Genovese
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Abstract

We study the isotropic XY quantum spin chain with a time-periodic transverse magnetic field acting on a single site. The asymptotic problem can be mapped into a highly resonant Floquet-Schrödinger equation, for which, under a diophantine-like assumption on the frequency, we show the existence of a periodic solution. The proof is based on a KAM-type renormalisation. This in turn implies the state of the quantum spin chain to be asymptotically a periodic function synchronised with the forcing also at low frequencies.

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Livia Corsi, Giuseppe Genovese. 2020-12-13. Long time behaviour of a local perturbation in the isotropic XY chain under periodic forcing. https://arxiv.org/abs/1908.09035

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