Georgia Institute of Technology College of Sciences

I will consider the isotropic XY quantum chain with a transverse magnetic field acting on a single site and analyze the long time behaviour of the time-dependent state of the system when a periodic perturbation drives the impurity. 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 potential is small enough then for large enough frequencies the state approaches a periodic orbit synchronized with the potential. Moreover I will provide the explicit rate of convergence to the asymptotics. This is a joint work with G. Genovese.