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

Livia Corsi
Georgia Tech. Atlanta
Monday, June 4, 2018 - 14:30

I will consider the isotropic XY quantum chain with a periodic transverse magnetic field acting on a single site and analyze the long time behaviour of the state of the system. It has been shown in the early 70’s that, in the thermodynamic limit, the state of such system obeys a linear time-dependent Schrodinger equation with a memory term. I will consider two different regimes, namely when the perturbation has non-zero or zero average, and I will show that if the magnitute of the forcing is small enough then for large enough frequencies the state approaches a periodic orbit synchronized with the forcing. Moreover I will provide the explicit rate of convergence to the asymptotics. This is a joint work with G. Genovese.

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