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

TL;DR

This paper investigates how a high-frequency periodic drive on an impurity in the isotropic XY chain causes the system's state to synchronize with the forcing, providing explicit convergence rates.

Contribution

It offers a detailed analysis of the long-term behavior of the system under high-frequency periodic driving, including explicit convergence rates to the synchronized state.

Findings

System approaches a periodic orbit at high frequencies

Explicit rate of convergence to the asymptotic state

Synchronization with the periodic forcing

Abstract

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