Scaling behaviour of the relaxation in quantum chains

We consider the nonequilibrium time evolution of the transverse magnetization in the critical Ising and XX quantum chains. For some inhomogeneously magnetized initial states we derive analytically the transverse magnetization profiles and show that they evolve into scaling forms in the long-time limit. In particular it is seen that the Ising chain exhibits some similarities with the conserved dynamics XX chain. That is, after a transient regime, the total residual magnetization in the transverse direction is also conserved in the Ising case. A class of general initial states is also considered